6.47 Given the following probabilities, compute all joint probabilities.

d. Find the probability of no right-handers, one right-hander, two right-handers, three right- handers.

6.54 Suppose there are 100 students in your accounting class, 10 of whom are left-handed. Two students are selected at random. a. Draw a probability tree and insert the probabili-

ties for each branch.

What is the probability of the following events? b. Both are right-handed. c. Bothareleft-handed.

One is right-handed and the other is left-handed.

At least one is right-handed

6.55 Refer to Exercise 6.54. Suppose that three people are selected at random.

Draw a probability tree and insert the probabili-

ties of each branch.

What is the probability of no right-handers, one

right-hander, two right-handers, three right- handers?

6.56 An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 40% probability of winning the first contract. If they win the first contract, the probability of winning the sec- ond is 70%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 50%.

What is the probability that they win both con- tracts?

What is the probability that they lose both con- tracts?

What is the probability that they win only one contract?

6.57 A telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 20% of her calls, there is no answer or the line is busy. She sells subscriptions to 5% of the remaining calls. For what proportion of calls does she make a sale?

P(A) = .9 P(BA) = .4

P(AC) = .1 P(BAC) = .7

6.48 Determinealljointprobabilitiesfromthefollowing. P(A) = .8 P(AC) = .2

P(BA) = .4 P(BAC) = .7

6.49 Draw a probability tree to compute the joint proba-

bilities from the following probabilities. P(A) = .5 P(AC) = .2

P(BA) = .4 P(BAC) = .7

6.50 Giventhefollowingprobabilities,drawaprobability

tree to compute the joint probabilities. P(A) = .8 P(AC) = .2

P(BA) = .3 P(BAC) = .3

6.51 Given the following probabilities, find the joint

probability P(A and B). P(A) = .7 P(BA) = .3

6.52 Approximately 10% of people are left-handed. If two people are selected at random, what is the prob- ability of the following events? a. Bothareright-handed.

b. Both are left-handed. c. Oneisright-handedandtheotherisleft-handed. d. At least one is right-handed.

6.53 Refer to Exercise 6.52. Suppose that three people are selected at random.

Draw a probability tree to depict the experiment.

If we use the notation RRR to describe the selec-

tion of three right-handed people, what are the descriptions of the remaining seven events? (Use L for left-hander.)

How many of the events yield no right-handers, one right-hander, two right-handers, three right- handers?

6.58 A foreman for an injection-molding firm admits that on 10% of his shifts, he forgets to shut off the injec- tion machine on his line. This causes the machine to overheat, increasing the probability from 2% to 20% that a defective molding will be produced dur- ing the early morning run. What proportion of moldings from the early morning run is defective?

6.59 A study undertaken by the Miami-Dade Supervisor of Elections in 2002 revealed that 44% of registered voters are Democrats, 37% are Republicans, and 19% are others. If two registered voters are selected at random, what is the probability that both of them have the same party affiliation? (Source: Miami Herald, April 11, 2002.)

6.60 In early 2001, the U.S. Census Bureau started releas- ing the results of the 2000 census. Among many other pieces of information, the bureau recorded the race or ethnicity of the residents of every county in every state. From these results, the bureau calculated a "diversity index" that measures the probability that two people chosen at random are of different races or ethnicities. Suppose that the census determined that in a county in Wisconsin 80% of its residents are white, 15% are black, and 5% are Asian. Calculate the diversity index for this county.

6.61 A survey of middle-aged men reveals that 28% of them are balding at the crown of their heads. Moreover, it is known that such men have an 18% probability of suffering a heart attack in the next 10 years. Men who are not balding in this way have an 11% probability of a heart attack. Find the prob- ability that a middle-aged man will suffer a heart attack sometime in the next 10 years.

6.62 The chartered financial analyst (CFA) is a designa- tion earned after a candidate has taken three annual exams (CFA I, II, and III). The exams are taken in early June. Candidates who pass an exam are eligible to take the exam for the next level in the following year. The pass rates for levels I, II, and III are .57, .73, and .85, respectively. Suppose that 3,000 candidates take the level I exam, 2,500 take the level II exam, and 2,000 take the level III exam. Suppose that one student is selected at random. What is the probability that he or she has passed the exam? (Source: Institute of Financial Analysts.)

6.63 TheNickelsrestaurantchainregularlyconductssur- veys of its customers. Respondents are asked to assess food quality, service, and price. The responses are

Excellent Good Fair

Surveyed customers are also asked whether they would come back. After analyzing the responses, an expert in probability determined that 87% of cus- tomers say that they will return. Of those who so

indicate, 57% rate the restaurant as excellent, 36% rate it as good, and the remainder rate it as fair. Of those who say that they won't return, the probabili- ties are 14%, 32%, and 54%, respectively. What proportion of customers rate the restaurant as good?

6.64 Researchers at the University of Pennsylvania School of Medicine have determined that children under 2 years old who sleep with the lights on have a 36% chance of becoming myopic before they are 16. Children who sleep in darkness have a 21% proba- bility of becoming myopic. A survey indicates that 28% of children under 2 sleep with some light on. Find the probability that a child under 16 is myopic.

6.65 All printed circuit boards (PCBs) that are manufac- tured at a certain plant are inspected. An analysis of the company's records indicates that 22% of all PCBs are flawed in some way. Of those that are flawed, 84% are reparable and the rest must be discarded. If a newly produced PCB is randomly selected, what is the probability that it does not have to be discarded?

6.66 A financial analyst has determined that there is a 22% probability that a mutual fund will outperform the market over a 1-year period provided that it out- performed the market the previous year. If only 15% of mutual funds outperform the market during any year, what is the probability that a mutual fund will outperform the market 2 years in a row?

6.67 An investor believes that on a day when the Dow Jones Industrial Average (DJIA) increases, the prob- ability that the NASDAQ also increases is 77%. If the investor believes that there is a 60% probability that the DJIA will increase tomorrow, what is the probability that the NASDAQ will increase as well?

6.68 Thecontrolsofanairplanehaveseveralbackupsys- tems or redundancies so that if one fails the plane will continue to operate. Suppose that the mecha- nism that controls the flaps has two backups. If the probability that the main control fails is .0001 and the probability that each backup will fail is .01, what is the probability that all three fail to operate?

6.69 According to TNS Intersearch, 69% of wireless web users use it primarily for receiving and sending e-mail. Suppose that three wireless web users are selected at random. What is the probability that all of them use it primarily for e-mail?

6.70 A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 25%. She also believes that if the econ- omy encounters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession, the probability that the mutual fund will increase in value is 75%. Find the probability that the mutual fund's value will increase.