Expand Your Knowledge: Conditional Probability
Expand Your Knowledge: Conditional Probability Pyramid Lake is located in Nevada on the Paiute Indian Reservation. This lake is famous for large cutthroat trout. The mean number of trout (large and small) caught from a boat is 0.667 fish per hour (Reference: Creel Chronicle, Vol. 3, No. 2). Suppose you rent a boat and go fishing for 8 hours. Let r be a random variable that represents the number of fish you catch in the 8-hour period.
(a)    Explain why a Poisson probability distribution is appropriate for r. What is l for the 8-hour fishing trip? Round l to the nearest tenth so that you can use Table 4 of Appendix II for Poisson probabilities.
(b)   If you have already caught three trout, what is the probability you will catch a total of seven or more trout? Compute P(r > 7 | r > 3). See Hint below.
(c)    If you have already caught four trout, what is the probability you will catch a total of fewer than nine trout? Compute P(r 6 9 | r > 4). See Hint below.
(d)Â Â Â List at least three other areas besides fishing to which you think conditional Poisson probabilities can be applied.
Hint for solution:Â Review item 6, conditional probability, in the summary of basic probability rules at the end of Section 4.2. Note that
P(A and B)
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P(AÂ 0Â Â Â B) =
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P(B)
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and show that in part  (b),
P((r > 7) and (r > 3))
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P(r > 7)
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P(r > 7 0    r > 3) =
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=
P(r > 3)
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P(r > 3)
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