1 The probability that a man will be alive in 10 years is 0.8 and the probability that his wife will be alive in 10 years is 0.9. Find the probability that in 10 years: (i) Both will be alive; (ii) Only the man will be alive; (iii) Only the wife will be alive; (iv) At least one will be alive.
1 The probability that a man will be alive in 10 years is 0.8 and the probability that his wife will be alive in 10 years is 0.9. Find the probability that in 10 years: (i) Both will be alive; (ii) Only the man will be alive; (iii) Only the wife will be alive; (iv) At least one will be alive.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Basic probability theory 51
Problems
1 The probability that a man will be alive in 10 years is 0.8 and the probability
that his wife will be alive in 10 years is 0.9. Find the probability that in 10
years:
(i) Both will be alive;
(ii) Only the man will be alive;
(iii) Only the wife will be alive;
(iv) At least one will be alive.
2 The probability of Inspector #1 on a production line finding a defective item
is 0.8 and of Inspector # 2, down the line, 0.7. What is the probability of a
defective item getting through?
3 Three urns contain, respectively, 1 white and 2 black balls, 2 white and 1
black balls, 2 white and 2 black balls. A blindfold man transfers one ball from
the first urn into the second, then one ball from the second urn into the third.
A ball is drawn from the third urn. What is the probability of its being white?
4 A worker operates three machines. The probability that for the duration of an
hour a machine does not require the attention of the worker is 0.9 for the first
machine, 0.8 for the second and 0.85 for the third. What is the probability that
in any one hour none of the machines require his attention? What is the
probability that at least one of the machines does not require any attention
during any one hour?
5 Two dice are tossed together. Let A be the event that the sum of the faces are
odd, B the event that at least one is a one. What is the probability that:
(a) Both A and B occur;
(b) Either A or B or both occur;
(c) A and not B occurs;
(d) B and not A occurs?
6 A box contains a normal coin and a two headed coin. A coin is selected at
random and tossed. If heads appear, the other coin is tested, if tails appear,
the same coin is tossed.
(a) Find the probability that heads appear on the second toss.
(b) If heads appeared on the second toss, find the probability that it also
appeared on the first toss.
7 A shopper buys two cartons of a dozen eggs each. His habit is to inspect 3
eggs picked at random from each carton and to reject the carton if he finds
one or more cracked eggs. If the first carton contains two cracked eggs and the
second, one cracked egg, find the probability that:
(a) Carton 1 is rejected and carton 2 is accepted.
(b) Both cartons are accepted.
(c) Neither carton is accepted.
8 A piece of equipment contains six identical items and it is known that three of
them are defective. The items are tested one after the other until the three
defective items are found.
(a) What is the probability that the testing process is stopped on the (i) third
test (ii) fourth test.
(b) If the process is stopped on the fourth test, what is the probability that
the first item is not defective.
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2 The probability of Inspector #1 on a production line finding a defective item is 0.8 and of Inspector #2, down the line, 0.7. What is the probability of a defective item getting through?
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