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A pond holds 4 fish. Each day a fisherman goes fishing and his probability of catching K = 0,1,2,3,4 fish that day follows a binomial PDF with p = 1/2.How many days should he plan on fishing so that the probability of his catching all 4 fish exceeds 0.9?

Can someone just give a hint on how to start thinking to solve this problem.

Taru Garg
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1 Answers1

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Hint:

If $X_1,X_2,X_3,\dots$ is a an iid sequence of random variables with binomial distribution with parameters $4$ and $0.5$ then $X_1+\cdots+X_k$ has binomial distribution with parameters $4k$ and $0.5$.

To be found here is the smallest $k$ that satisfies: $$P(X_1+\cdots+X_k\geq4)>0.9$$

drhab
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