202 Chapter 5 Probability 5–128. Find the probability of getting a full house (three 5–131. Find the probability of getting any triple-digit cards of one denomination and two of another) when five number, where all the digits are the same, on a lotto that cards are dealt from an ordinary deck. consists of selecting a three-digit number. 5–129. A committee of four people is to be formed from 5–132. Find the probability of selecting three science six doctors and eight dentists. Find the probability that the books and four math books from eight science books and committee will consist of the following: nine math books. The books are selected at random. a. All dentists 5–133. When three dice are rolled, find the probability of b. Two dentists and two doctors getting a sum of 7. c. All doctors d. Three doctors and one dentist 5–134. Find the probability of randomly selecting two e. One doctor and three dentists mathematics books and three physics books from four mathematics books and eight physics books from a box. 5–130. An insurance sales representative selects three policies to review. The group of policies he can select from 5–135. Find the probability that if five different-sized contains eight life policies, five automobile policies, and washers are arranged in a row, they will be arranged in two homeowner’s policies. Find the probability of selecting order of size. the following: 5–136. Using the information in Exercise 4–69, Chapter 4, a. All life policies find the probability of each poker hand. b. Both homeowner’s policies a. Royal flush c. All automobile policies b. Straight flush d. One of each policy c. Four of a kind e. Two life and one automobile policies 5–6 In this chapter, the basic concepts and rules of probability are explained. The three types of probability are classical, empirical, and subjective. Classical probability uses sample Summary spaces. Empirical probability uses frequency distributions and is based on observation. In subjective probability, the researcher makes an educated guess about the chance of an event occurring. A probability event consists of one or more outcomes of a probability experiment. Two events are said to be mutually exclusive if they cannot occur at the same time. Events can also be classified as independent or dependent. If events are independent, whether or not the first event occurs does not affect the probability of the next event oc- curring. If the probability of the second event occurring is changed by the occurrence of the first event, then the events are dependent. The complement of an event is the set of outcomes in the sample space that are not included in the outcomes of the event itself. Complementary events are mutually exclusive. Probability problems can be solved by using the addition rules, the multiplication rules, and the complementary event rules. Finally, when the number of outcomes of the sample space is large, probability problems can be solved by using the counting rules in Chapter 4. Important Terms classical probability 171 empirical mutually exclusive simple event 171 complement of an probability 175 events 182 subjective event 174 equally likely events 171 outcome 168 probability 178 compound event 171 event 171 probability 168 Venn diagrams 175 conditional independent events 188 probability probability 191 law of large experiment 168 dependent events 190 numbers 178 sample space 168 Section 5–6 Summary 203 Important Formulas Formula for classical probability: Addition rule 2, for events that are not mutually exclusive: number of P(A or B) ϭ P(A) ϩ P(B) Ϫ P(A and B) outcomes Multiplication rule 1, for independent events: in E nΘEΙ PΘEΙ ϭ ϭ total number of nΘSΙ P(A and B) ϭ P(A) • P(B) outcomes in the Multiplication rule 2, for dependent events: sample space P(A and B) ϭ P(A) • P(B͉A) Formula for empirical probability: Formula for conditional probability: frequency for the class f PΘA and BΙ PΘEΙ ϭ ϭ PΘBԽAΙ ϭ total frequencies n PΘAΙ in the distribution Formula for complementary events: — — Addition rule 1, for two mutually exclusive events: PΘE Ι ϭ 1 Ϫ PΘEΙ or PΘEΙ ϭ 1 Ϫ PΘEΙ — P(A or B) ϭ P(A) ϩ P(B) or PΘEΙ ϩ PΘEΙ ϭ 1 Review Exercises 5–137. When a die is rolled, find the probability of getting b. A yellow or a white sweater a. A5 c. A red, a blue, or a yellow sweater b. A6 d. A sweater that was not white c. A number less than 5 5–143. At a swimwear store, the managers found that 5–138. When a card is selected from a deck, find the 16 women bought white bathing suits, 4 bought red suits, probability of getting 3 bought blue suits, and 7 bought yellow suits. If a a. A club customer is selected at random, find the probability that b. A face card or a heart she bought the following. c. A 6 and a spade a. A blue suit d. A king b. A yellow or a red suit e. A red card c. A white or a yellow or a blue suit d. A suit that was not red 5–139. In a survey conducted at a local restaurant during breakfast hours, 20 people preferred orange juice, 16 5–144. When two dice are rolled, find the probability of preferred grapefruit juice, and 9 preferred apple juice with getting breakfast. If a person is selected at random, find the a. A sum of 5 or 6 probability that he or she prefers grapefruit juice. b. A sum greater than 9 c. A sum less than 4 or greater than 9 5–140. If a die is rolled one time, find these probabilities: d. A sum that is divisible by 4 a. Getting a 5 e. A sum of 14 b. Getting an odd number f. A sum less than 13 c. Getting a number less than 3 5–145. The probability that a person owns a car is 0.80, 5–141. A recent survey indicated that in a town of 1500 that a person owns a boat is 0.30, and that a person owns households, 850 had cordless telephones. If a household is both a car and a boat is 0.12. Find the probability that a randomly selected, find the probability that it has a cordless person owns either a boat or a car, but not both. telephone. 5–146. There is a 0.39 probability that John will purchase 5–142. During a sale at a men’s store, 16 white sweaters, 3 a new car, a 0.73 probability that Mary will purchase a red sweaters, 9 blue sweaters, and 7 yellow sweaters were new car, and a 0.36 probability that both will purchase a purchased. If a customer is selected at random, find the new car. Find the probability that neither will purchase probability that he bought the following: a new car. a. A blue sweater 204 Chapter 5 Probability 5–147. A Gallup Poll found that 78% of Americans 5–155. The probability that Sue will live on campus and worry about the quality and healthfulness of their diet. If buy a new car is 0.37. If the probability that she will live on five people are selected at random, find the probability campus is 0.73, find the probability that she will buy a new that all five worry about the quality and healthfulness of car, given that she lives on campus. their diet. 5–156. The probability that a customer will buy a Source: The Book of Odds by Michael D. Shook and Robert C. television set and buy an extended warranty is 0.03. If the Shook (New York: Penguin Putnam, Inc., 1991), p. 33. probability that a customer will purchase a television set is 0.11, find the probability that the customer will also 5–148. Twenty-five percent of the engineering graduates purchase the extended warranty. of a university received a starting salary of $25,000 or more. If three of the graduates are selected at random, 5–157. Of the members of the Blue River Health Club, find the probability that all had a starting salary of $25,000 43% have a lifetime membership and exercise regularly or more. (three or more times a week). If 75% of the club members exercise regularly, find the probability that a randomly 5–149. Three cards are drawn from an ordinary deck selected member is a life member, given that he or she without replacement. Find the probability of getting exercises regularly. a. All black cards b. All spades 5–158. The probability that it snows and the bus arrives c. All queens late is 0.023. John hears the weather forecast, and there is a 40% chance of snow tomorrow. Find the probability that 5–150. A coin is tossed and a card is drawn from a deck. the bus will be late, given that it snows. Find the probability of getting a. A head and a 6 5–159. A number of students were grouped according to b. A tail and a red card their reading ability and education. The table shows the c. A head and a club results. 5–151. A box of candy contains six chocolate-covered Reading ability cherries, three peppermint patties, two caramels, and two Education Low Average High strawberry creams. If a piece of candy is selected, find the probability of getting a caramel or a peppermint patty.