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

2. Sample Space The set of all possible outcomes!
Answer question 1
On your paper, list all the events possible for tossing 2 dice.

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

4. Answer question 2 Answer question 3
List possibilities, then narrow down to sample space based on restrictions of the question.
Answer question 3

5. What you want divided by the total.
Probability !
What you want divided by the total.

6. 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

7. What is the probability of event F, “rolling a sum of five” on a toss of two dice?
Answer question 4

8. 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

9. Disjoint or Mutually Exclusive
Events from the same sample space that have no outcomes in common
Rolling doubles or a sum of 7

10. 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

11. 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

12. 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).

13. 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

14. 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

15. 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?

16. 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

17. 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

18. 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