Conditional Probability P-7 Probability Conditional Probability
WHAT YOU WILL LEARN • How to determine probability under a given set of conditions
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).
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.
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
Solutions (continued) two girls given that the older child is a girl
Conditional Probability For any two events, E1 and E2,
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:
Example (continued) a) prefers peppermint b) is a woman
Example (continued) c) prefers peppermint, given that a woman is selected d) is a man, given that the person prefers wintergreen
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
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.
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.
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.
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.
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.
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.
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.
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.