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**Beginning Probability**

Sample space Event Disjoint or Mutually Exclusive Complement of an Event Independent Events Binomial Probability Empirical vs Theoretical Probability

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**Sample Space The set of all possible outcomes!**

Answer question 1 On your paper, list all the events possible for tossing 2 dice.

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An Event Any one or combinations of possible outcomes – a subset of the sample space.

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**Answer question 2 Answer question 3**

List possibilities, then narrow down to sample space based on restrictions of the question. Answer question 3

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**What you want divided by the total.**

Probability ! What you want divided by the total.

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**An impossible event An certain event**

Roll a 7 on one die P(E) = 0 An certain event Flip a head or tail P(E) = 1

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**What is the probability of event F, “rolling a sum of five” on a toss of two dice?**

Answer question 4

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**What is the sample space? (think of the F.C.P. – ways to count)**

What is the probability that a five-digit telephone number chosen at random has no repeated digits? What is the sample space? (think of the F.C.P. – ways to count) n(S) = _ _ _ _ _ = What events do you want? n(E) = _ _ _ _ _ = Answer question 5

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**Disjoint or Mutually Exclusive**

Events from the same sample space that have no outcomes in common Rolling doubles or a sum of 7

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**Disjoint or Mutually Exclusive**

If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B). Notice the key work “or” Rolling doubles or a sum of 7 Answer question 6

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**Packy randomly chooses a digit between 0 and 9 (inclusive)**

Packy randomly chooses a digit between 0 and 9 (inclusive). What is the probability that Packy will choose a digit that is greater than 6 or is a multiple of 6? What’s the sample space? n(S) = Answer question 7

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**If A is an event, then the probability that A does not occur is**

Complement of an Event The complement of the event A, denoted Ac, is the set of all outcomes in the sample space that are not in event A. If A is an event, then the probability that A does not occur is P(AC) = 1 – P(A).

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Complement of an Event If A is an event, then the probability that A does not occur is P(AC) = 1 – P(A). A = a digit that is greater than 6 or is a multiple of 6 then P(Ac) = Look at all the events that aren’t part of A n(S) = Answer question 8

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**Answer question 9 Answer question 10**

In the game of contract bridge, each player is dealt a 13-card hand from a standard deck of 52 cards. What is the probability that a bridge hand has at least 1 heart? Answer question 9 Answer question 10

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**Getting an A in stats and an A in english Can you think of any more?**

Independent Events Two events are independent events if the occurrence of one has no effect on the probability of the occurrence of the other. Flip a coin twice Roll 2 dice or 1 dice twice Getting an A in stats and an A in english Can you think of any more?

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**Independent Events or means + and means x**

If A and B are independent events, then P(A and B) = P(A) * P(B) Notice the key word “and” You develop a program to generate random digits. What is the probability that the first digit generated is even and the second is a multiple of 3? Are the two events independent? n(S) = Answer question 11 Answer question 12 Answer question 13

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**n(S) = H, T Answer question 14**

What is the probability of the outcome HTH when a coin is tossed three times? n(S) = H, T Answer question 14

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**Empirical vs Theoretical Probability**

The probability you get when you experiment vs the probability the formulas say you get. Tossing a coin 20 times to see % of Heads Vs Calculating P(H) with the formula

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