FM Dept Review Part 2 - Faculty Web Pages

Lial 9 th Edition
FM Dept Review P2 F09
20. A bicycle factory runs two assembly lines, A and B. 97% of line A’s products pass inspection and 94% of
line B’s products pass inspection. 50% of the factory’s bikes come off assembly line B and the rest come
off line A. Find the probability that one of the factory’s bikes did not pass inspection and came off assembly
line B. Write your answer as a decimal. 7.5.41
21. In 2002, 66.5% of men and 50.1% of women in a country were overweight. Given that 48.6% of adults are
men and 51.4% are women, find the probability that a randomly selected adult fits the following
descriptions. 7.5.61
a. An overweight man
b. Overweight
c. Are the events that an adult is a man and that an adult is overweight independent? Explain.
22. If it snows tomorrow, the probability is 0.7 that John will practice his trombone. If it does not snow
tomorrow, there is only a 0.5 chance that John will practice. Suppose the chance of snow tomorrow is 50%.
What is the probability that John will practice his trombone? 7.5.71
23. Suppose 25% of the population is 63 or over, 27% of those 63 or over have loans, and 54% of those
under 63 have loans. Find the probabilities that a person fits into the following categories. Write your
answers as a decimal rounded to three decimal places. 7.5.77
a. The probability that a person is 63 or over and has a loan is ____________________.
b. The probability that a person has a loan is ____________________.
On problems 24 – 27, make sure to show your tree diagram.
24. Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 2 black balls. Jar 2 has 4
white balls and 1 black ball. Jar 3 has 1 white ball and 2 black balls. One jar is to be selected and then 1
ball is to be drawn from the selected jar. The probability of selecting the first, second, and third jars are 1/3,
1/2 , and 1/6 respectively. Find the probability the ball was drawn from Jar 2 given that the ball was white.
Write your answer as a simplified fraction. 7.6.7
25. Of all the people applying for a certain job, 90% are qualified and 10% are not. The personnel manager
claims that she approves qualified people 90% of the time; she approves unqualified people 20% of the
time. Find the probability that a person is qualified if he or she was not approved by the manager. Write
your answer as a decimal rounded to 3 decimal places if necessary. 7.6.11
26. A manufacturer obtains clock-radios from three different subcontractors: 40% from A, 10% from B, and
50% from C. The defective rates for these subcontractors are 1%, 4%, and 4% respectively. If a defective
clock-radio is returned by a customer, what is the probability that is came from: 7.6.21
a. subcontractor A? Round your decimal answer to three places, if necessary.
b. subcontractor B? Round your decimal answer to three places, if necessary.
c. subcontractor C? Round your decimal answer to three places, if necessary.
27. A new lie-detector test has been devised and must be tested before it is put into use. Three hundred
people are selected at random, and each person draws and keeps a card from a box of 300 cards. Half the
cards instruct the person to lie and the others instruct the person to tell the truth. Of those who lied, 80%
fail the new lie-detector test (that is the test indicated lying). Of those who told the truth, 4% failed the test.
7.6.29
a. What is the probability that a randomly chosen subject will have lied given that the subject failed the test.
Round your answer to 4 decimal places as necessary.
b. What is the probability that the subject will not have lied given that the subject failed the test? Round your
answer to 4 decimal places as necessary.
28. A man has 8 shirts and 4 ties. How many different shirt and tie arrangements can he wear? 8.1.15
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