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1A.

Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2000. Color: Silver White Black Dark green Dark blue Medium red Probability: 0.177 0.173 0.118 0.088 0.087 0.062 [a) What is the probability that the vehicle you choose has any color other than the six listed? [b) What is the probability that a randomly chosen vehicle is either silver or white? (c) Choose two vehicles at random. What is the probability that both are silver or white?The 2000 census allowed each person to choose one or more from a long list of races. That is, in the eyes of the Census Bureau, you belong to whatever race or races you say you belong to. "Hispanic/Latino" is a separate category; Hispanics may be of any race. If we choose a resident of the United States at random, the 200 census gives the following probabilities. Hispanic Not Hispanic Asian 0.003 0.033 Black 0.003 0.121 White 0.020 0.731 Other 0.068 0.021 Let A be the event that a randomly chosen American is Hispanic, and let 8 be the event that the person chosen is white. (a) Verify that the table gives a legitimate assignment of probabilities. (Choose all that apply.) O The sum of all 8 probabilities equals 1. O Not all probabilities satisfy 0 S p S 1. O All probabilities satisfy 0 S p S 1. O The sum of all 8 probabilities does not equal 1. (b) What is P(A)? (c) Describe B" in words. O The chosen person is white. O The chosen person is black. The chosen person is not black. O The chosen person is not white. Find P(B") by the complement rule. (d) Express "the chosen person is a non-Hispanic white" in terms of events A and B. OB'nA OA'nB O An BC OAnB What is the probability of this event?Probabilities are assigned for the ethnic background of a randomly chosen resident of the United States. Hispanic Not Hispanic Asian 0.003 0.033 Black 0.006 0.118 White 0.020 0.731 Other 0.061 0.028 Let A be the event that the person chosen is Hispanic, and let B be the event that he or she is white. Are events A and B independent? O Yes O No How do you know? O P(A) x P(B) = P(A U B). O P(A) x P(B) = P(An B). O P(A) x P(B) - P(AnB). O P(A) x P(B) - P(A U B).Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Census Bureau, P(A) = 0.138, P(B) = 0.254, and the joint probability that a household is both prosperous and educated is P(A and B) = 0.081. What is the probability P(A or B) that the household selected is either prosperous or educated?Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Census Bureau, P(A) = 0.135, P(B) = 0.254, and the joint probability that a household is both prosperous and educated is P(A and B) = 0.085. Draw a Venn diagram that shows the relation between events A and B. (Do this on paper. Your instructor may ask you to turn in the work.) Indicate each of the following events on your diagram and use the information to calculate the probability of each event. Finally, describe in words what each event is. (a) {A and B'} O represents both prosperous and educated O represents prosperous but not educated O represents not prosperous but educated O represents neither prosperous nor educated P(A and B) = (b) {A and B } O represents both prosperous and educated O represents prosperous but not educated O represents not prosperous but educated O represents neither prosperous nor educated P(A and BS) = (c) {AC and B} O represents both prosperous and educated O represents prosperous but not educated O represents not prosperous but educated O represents neither prosperous nor educated P(AC and B) = (d) {AC and By} O represents both prosperous and educated O represents prosperous but not educated O represents not prosperous but educated O represents neither prosperous nor educated P(A and B-) =Consolidate Builders has bid on two large construction projects. The company president believes that the probability of winning the first contract (event A) is 0.4 that the probability of winning the secon (event B) is 0.5, and that the joint probability of winning both jobs (event {A and B)) is 0.2. Are events A and B independent? Do a calculation that proves your answer. O Yes O NoRamon has applied to both Princeton and Stanford. He thinks the probability that Princeton will admit him is 0.6, the probability that Stanford will admit him is 0.5, and the probability that both will admit him is 0.4. (a) Make a Venn diagram with the probabilities given marked. (Do this on paper. Your instructor may ask you to turn in your work.) (b) What is the probability that neither university admits Ramon? (c) What is the probability that he gets into Stanford but not Princeton?Choose an adult American woman at random. Table 6.1 describes the population from which we draw. Use the information in that table to answer the following questions. (a) What is the probability that the woman chosen is between 18-29? (b) What is the conditional probability that the woman chosen is married, given that she is between 18-29? (c) How many women are both married and in the over-65 age group? What is the probability that the woman we choose is a married woman at least 65 years old? TABLE 6.1 Age and marital status of women (thousands of women) Age 18-29 30-64 65 and over Total Married 7,842 43,808 8,270 59.920 Never married 13,930 7,184 751 21,865 Widowed 36 2,523 8,385 10,944 Divorced 704 9.174 1,263 11,141 Total 22,512 62,689 18,669 103,870 Source: Data for 1999 from the 2000 Statistical Abstract of the United States.Choose an employed person at random. Let A be the event that the person chosen is a woman, and B the event that the person holds a managerial or professional job. Government data tell us that P(A) = 0.41 and the probability of managerial and professional jobs among women is P(B|A) = 0.33. Find the probability that a randomly chosen employed person is a woman holding a managerial or professional position.A poker player holds a flush when all 5 cards in the hand belong to the same suit. We will find the probability of a flush when 5 cards are dealt. Remember that a deck contains 52 cards, 13 of each suit, and that when the deck is well shuffled, each card dealt is equally likely to be any of those that remain in the deck. (a) We will concentrate on diamonds. What is the probability that the first card dealt is a diamond? What is the conditional probability that the second card is a diamond, given that the first is a diamond? (b) Continue to count the remaining cards to find the conditional probabilities of a diamond on the third, the fourth, and the fifth card, given in each case that all previous cards are diamonds. Probability a diamond on the third a diamond on the fourth a diamond on the fifth (c) The probability of being dealt 5 diamonds is the product of the five probabilities you have found. Why? O This is guaranteed by the complement rule. O This is guaranteed by the multiplication rule. O This is guaranteed by the addition rule. What is this probability? (d) The probability of being dealt 5 hearts or 5 diamonds or 5 clubs is the same as the probability of being dealt 5 spades. What is the probability of being dealt a flush?You have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 7% of such operations, the repair fails in 18%, and both infection and failure occur together in 2%. What percent of these operations succeed and are free from infection? %The voters in a large city are 40% white, 30% black, and 30% Hispanic. (Hispanics may be of any race in official statistics, but in this case we are speaking of political blocks.) A black mayoral candidate anticipates attracting 30% of the white vote, 90% of the black vite, and 50% of the Hispanic vote. Draw a tree diagram with probabilities for the race (white, black, or Hispanic) and vote (for or against the candidate) of a randomly chosen voter. What percent of the overall vote does the candidate expect to get? %