ments. They claim the probability that he will win the first tournament is 0.4. If he wins the first tournament, they estimate the probability that he will also win the second is 0.2. They guess that if he loses the first tournament, the probability that he will win the second is 0.3. a) According to their estimates, are the two tournaments independent? Explain your answer. b) What's the probability that he loses both tournaments? c) What's the probability he wins both tournaments?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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27. Fishing tournament. A sporting goods manufacturer
was asked to sponsor a local boy in two fishing tourna-
ments. They claim the probability that he will win the first
tournament is 0.4. If he wins the first tournament, they
estimate the probability that he will also win the second
is 0.2. They guess that if he loses the first tournament, the
probability that he will win the second is 0.3.
a) According to their estimates, are the two tournaments
independent? Explain your answer.
b) What's the probability that he loses both tournaments?
c) What's the probability he wins both tournaments?
d) Let random variable X be the number of tournaments
he wins. Find the probability model for X.
e) What are the expected value and standard deviation
of X?
Transcribed Image Text:27. Fishing tournament. A sporting goods manufacturer was asked to sponsor a local boy in two fishing tourna- ments. They claim the probability that he will win the first tournament is 0.4. If he wins the first tournament, they estimate the probability that he will also win the second is 0.2. They guess that if he loses the first tournament, the probability that he will win the second is 0.3. a) According to their estimates, are the two tournaments independent? Explain your answer. b) What's the probability that he loses both tournaments? c) What's the probability he wins both tournaments? d) Let random variable X be the number of tournaments he wins. Find the probability model for X. e) What are the expected value and standard deviation of X?
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