1. AND

2. Chapter 12
Probability

3. WHAT YOU WILL LEARN
• Empirical probability and theoretical probability
• Compound probability, conditional probability, and binomial probability
• Odds against an event and odds in favor of an event
• Expected value
• Tree diagrams

4. WHAT YOU WILL LEARN • Mutually exclusive events and independent events
• The counting principle, permutations, and combinations

5. Conditional Probability
Section 7
Conditional Probability

6. Conditional Probability
In general, the probability of event E2 occurring, given that an event E1 has happened (or will happen; the time relationship does not matter), is called a conditional probability and is written P(E2|E1).

7. Example
Given a family of two children, and assuming that boys and girls are equally likely, find the probability that the family has
a) two girls.
b) two girls if you know that at least one of the children is a girl.
c) two girls given that the older child is a girl.

8. Solutions
a) two girls
There are four possible outcomes BB, BG, GB, and GG.
b) two girls if you know that at least one of the children is a girl

9. Solutions (continued)
two girls given that the older child is a girl

10. Conditional Probability
For any two events, E1 and E2,

11. Example 257 127 130 Total 132 72 60 Women 125 55 70 Men Prefers
Wintergreen
Prefers Peppermint
Use the results of the taste test given at a local mall. If one person from the sample is selected at random, find the probability the person selected:

12. Example (continued)
a) prefers peppermint
b) is a woman

13. Example (continued)
c) prefers peppermint, given that a woman is selected
d) is a man, given that the person prefers wintergreen