1. Conditional Probability
P-7 Probability
Conditional Probability

2. WHAT YOU WILL LEARN
• How to determine probability under a given set of conditions

3. 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).

4. 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.

5. 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

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

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

8. 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:

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

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

11. The local elementary school cafeteria offered ham sandwiches and pizza for lunch one day. The number of boys and girls who ate either a ham sandwich or pizza were recorded. The results are shown below.
Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218

12. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the student is a boy.
a. b. c. d.

13. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the student is a boy.
a. b. c. d.

14. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the student ate pizza for lunch.
a. b. c. d.

15. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the student ate pizza for lunch.
a. b. c. d.

16. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the person ate a ham sandwich for lunch, given that they are a girl.
a. b. c. d.

17. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the person ate a ham sandwich for lunch, given that they are a girl.
a. b. c. d.

18. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the person is a boy, given that they ate pizza for lunch.
a. b. c. d.

19. Ham
Sandwich
Pizza
Total
Boys 40 62
102
Girls 28 88
116 68
150
218
If one of these students is selected at random, determine the probability that the person is a boy, given that they ate pizza for lunch.
a. b. c. d.