1. Dr. Fowler  AFM  Unit 7-8
Probability

2. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

3. Introduction to Probability:

4. Classical Probability
Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur.
P(Event) = the favorable number of outcomes
the number of possible outcomes
Example: A die is rolled.
Find the probability of Event A: rolling a 5.
There is one outcome in Event A: {5}
P(A) =
“Probability of Event A.”

5. Empirical Probability
Empirical (or statistical) probability is based on observations obtained from probability experiments. The empirical frequency of an event E is the relative frequency of event E.
Example:
A travel agent determines that in every 50 reservations she makes, 12 will be for a cruise.
What is the probability that the next reservation she makes will be for a cruise?
P(cruise) =

6. Definition – a probability model will always have: 1) positive values & 2) total values adding up to 1

7. S = 8 Total outcomes listed
Calculate the probability that in a 3 child family there are 2 boys and 1 girl. Assume equally likely outcomes.
E = All outcomes with 2 Boys & 1 Girl
= { BBG, BGB, GBB } = 3 Total
S = 8 Total outcomes listed

8. The Addition Rule – Mutually Exclusive
Example: You roll a die. Find the probability that you roll a number less than 3 or a 4.
The events are mutually exclusive.
P (roll a number less than 3 or roll a 4)
= P (number is less than 3) + P (4)

9. The Addition Rule – Not Mutually Exclusive
Example:
A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart.
The events are not mutually exclusive because the Jack of hearts can occur in both events.
P (select a Jack or select a heart)
= P (Jack) + P (heart) – P (Jack of hearts)

10. Complementary Events
The complement of Event E is the set of all outcomes in the sample space that are not included in event E. (Denoted E′ and read “E prime.”)
P(E) + P (E′ ) = 1
P(E) = 1 – P (E′ )
P (E′ ) = 1 – P(E)
Example:
There are 5 red chips, 4 blue chips, and 6 white chips in a basket. Find the probability of randomly selecting a chip that is not blue.
P (selecting a blue chip)
P (not selecting a blue chip)

11. On the local news the weather reporter stated that the probability of rain tomorrow is 30%. What is the probability that it will not rain?

12. Multiplication Rule Example: A die is rolled and two coins are tossed.
Find the probability of rolling a 5, and flipping two tails.
P (rolling a 5) =
Whether or not the roll is a 5, P (Tail ) =
so the events are independent.
P (5 and T and T ) = P (5)· P (T )· P (T )

13. Notice – sum of probabilities is 1

14. Notice – sum of probabilities is 1

15. What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.

16. Excellent Job !!! Well Done