Samples spaces are _______________ Mutually exclusive events are _______________ Complementary events are _______________ Independent events are _______________ Compound events are _______________ Outcomes are _______________ Trials are _______________ Events are _______________ Probabilities are _______________ The probability of an event (E) is _______________ ‘And’ implies _________ in probability and is denoted _____. ‘Or’ implies _________ in probability and is denoted _____. Copy and complete each of these sentences in your note book.

Samples spaces are _______________ Mutually exclusive events are _______________ Complementary events are _______________ Independent events are _______________ Compound events are _______________ Outcomes are _______________ Trials are _______________ Events are _______________ Probabilities are _______________ The probability of an event (E) is _______________ ‘And’ implies _________ in probability and is denoted _____. ‘Or’ implies _________ in probability and is denoted _____. Copy and complete each of these sentences in your note book. Now scroll through the following slides add to or alter your responses so that you include all the information in the rest of this presentation.

1. Samples spaces are lists of all the possible outcomes from one or more trials

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments).

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….)

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*:

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. :

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die:

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die Green Die

1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 1, 2 1, 3 1, 4 1, 5 1, 6

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 1, 2 2, 2 1, 3 2, 3 1, 4 2, 4 1, 5 2, 5 1, 6 2, 6

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 1, 2 2, 2 3, 2 1, 3 2, 3 3, 3 1, 4 2, 4 3, 4 1, 5 2, 5 3, 5 1, 6 2, 6 3, 6

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 1, 2 2, 2 3, 2 4, 2 1, 3 2, 3 3, 3 4, 3 1, 4 2, 4 3, 4 4, 4 1, 5 2, 5 3, 5 4, 5 1, 6 2, 6 3, 6 4, 6

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 1, 2 2, 2 3, 2 4, 2 5, 2 1, 3 2, 3 3, 3 4, 3 5, 3 1, 4 2, 4 3, 4 4, 4 5, 4 1, 5 2, 5 3, 5 4, 5 5, 5 1, 6 2, 6 3, 6 4, 6 5, 6

(Might be a list or a tree diagram or a table or other….) 1. Samples spaces are lists of all the possible outcomes from one or more trials (experiments). (Might be a list or a tree diagram or a table or other….) Eg 1 Possible outcomes of rolling a single die*: 1, 2, 3, 4, 5, 6 * Unless told otherwise, assume the die is a fair, six-sided die with 1, 2, 3, 4, 5 and 6 as the equally likely outcomes. Eg 2 Possible outcomes of rolling a red die and a green die: Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

2. Mutually exclusive (ME) events are events that

2. Mutually exclusive (ME) events are events that cannot both happen.

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot.

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0.

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**,

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen.

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME.

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME. On the other hand,

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME. On the other hand, the outcomes drawing a club and

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME. On the other hand, the outcomes drawing a club and drawing a Jack

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME. On the other hand, the outcomes drawing a club and drawing a Jack can both happen

2. Mutually exclusive (ME) events are)events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME. On the other hand, the outcomes drawing a club and drawing a Jack can both happen (ie the Jack of clubs).

2. Mutually exclusive (ME) events are events that cannot both happen. If one happens, the other cannot. If A and B are ME, P(A and B) = 0. Eg When drawing a single card from a deck of cards**, the outcomes drawing a club and drawing a diamond in the one card cannot both happen. They are ME. On the other hand, the outcomes drawing a club and drawing a Jack can both happen (ie the Jack of clubs). ** Unless told otherwise, assume the deck of cards is a standard 52 card deck with no joker, 4 suites (the red suites – Hearts and Diamonds and the black suites - Clubs and Spades) and 13 cards in each suite – Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

3. Complementary events are mutually exclusive events

3. Complementary events are mutually exclusive events in which one of them will

3. Complementary events are mutually exclusive events in which one of them will definitely happen.

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary,

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B)

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1.

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A,

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (or, A’).

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black.

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black. P(Black) = 1/2

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black. P(Black) = 1/2 , P(Red) = 1/2

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black. P(Black) = 1/2 , P(Red) = 1/2 and

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black. P(Black) = 1/2 , P(Red) = 1/2 and P(Black)

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black. P(Black) = 1/2 , P(Red) = 1/2 and P(Black) + P(Red)

3. Complementary events are mutually exclusive events in which one of them will definitely happen. If A and B are complementary, P(A) + P(B) = 1. Also, if B is complementary to A, then B = Ā (A’). Eg When drawing a single card from a deck of cards drawing a black card and drawing a red card the outcomes are complementary because you are guaranteed that the card will be either red or black. P(Black) = 1/2 , P(Red) = 1/2 and P(Black) + P(Red) = 1.

4. Independent events are events which

4. Independent events are events which have no effect whatsoever

4. Independent events are events which have no effect whatsoever on the probability of each other happening.

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent,

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B).

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) =

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B).

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die.

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die.

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) =

If A and B are independent then P(A and B) = P(A)  P(B). 4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

If A and B are independent then P(A and B) = P(A)  P(B). 4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

If A and B are independent then P(A and B) = P(A)  P(B). 4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

If A and B are independent then P(A and B) = P(A)  P(B). 4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

If A and B are independent then P(A and B) = P(A)  P(B). 4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

If A and B are independent then P(A and B) = P(A)  P(B). 4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6 Note: we can denote the above as

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6 Note: we can denote the above as P(6 on red | 6 on green).

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6 Note: we can denote the above as P(6 on red | 6 on green). This thing

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6 (Note: we can denote the above as P(6 on red | 6 on green). This thing

4. Independent events are events which have no effect whatsoever on the probability of each other happening. If A and B are independent, then whether or not A happens has NO effect on P(B). If A and B are independent then P(A and B) = P(A)  P(B). Eg When rolling a red die and rolling a green die. What happens on one die has no effect on the outcome of the other die. P(6 on Red die) = 1/6 P(6 on Green die) = 1/6 P(6 on Red Die given that there was a 6 on the Green die) = 1/6 (Note: we can denote the above as P(6 on red | 6 on green). This thing means ‘given’

5. Compound events are when events are

5. Compound events are when events are combined

5. Compound events are when events are combined and we want to know the probability of both events happening

5. Compound events are when events are combined and we want to know the probability of both events happening or

5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening.

5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die.

5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) =

Eg When rolling a red die and rolling a green die. P(6 on both) = 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) (ie P(6 on red)xP(6 on green) = Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) (ie P(6 on red)xP(6 on green) = 1/6x1/6 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) (ie P(6 on red)xP(6 on green) = 1/6x1/6 because they are independent) Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) (ie P(6 on red)xP(6 on green) = 1/6x1/6 because they are independent) P(6 on either red or green die) = Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) (ie P(6 on red)xP(6 on green) = 1/6x1/6 because they are independent) P(6 on either red or green die) = 11/36 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

Eg When rolling a red die and rolling a green die. 5. Compound events are when events are combined and we want to know the probability of both events happening or of either event happening. Eg When rolling a red die and rolling a green die. P(6 on both) = 1/36 (ie P(6 on red and 6 on green) (ie P(6 on red)xP(6 on green) = 1/6x1/6 because they are independent) P(6 on either red or green die) = 11/36 Red Die 1 2 3 4 5 6 Green Die 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6

6. Outcomes are the results of experiments.

6. Outcomes are the results of experiments. 7. Trials are experiments.

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes.

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen (ie it is impossible)

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen (ie it is impossible) and a probability of 1 means

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen (ie it is impossible) and a probability of 1 means the event certainly will happen.

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen (ie it is impossible) and a probability of 1 means the event certainly will happen. The probability of an event (E) is denoted P(E) and is calculated by the formula:

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen (ie it is impossible) and a probability of 1 means the event certainly will happen. The probability of an event (E) is denoted P(E) and is calculated by the formula:

6. Outcomes are the results of experiments. 7. Trials are experiments. Events are desirable or favourable outcomes. 9. Probabilities are statements of likelihoods of certain outcomes occurring ranked such that a probability of 0 means the event certainly will not happen (ie it is impossible) and a probability of 1 means the event certainly will happen. The probability of an event (E) is denoted P(E) and is calculated by the formula: ***That is, the number of outcomes in the sample space

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted .

11. ‘And’ implies intersection in probability and is denoted . 12. Or’ implies union in probability and is denoted . You should now work on Ex 5D to 5H in your text. Some of the earlier exercises are very straightforward (but do make sure you can work up a sample space in any situation) and the later ones get quite complex so make so you spend a reasonable amount of time on them.