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Find the probability that a randomly picked cookie

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Correct the final answers to 4 decimal places whenever appropriate. A chef made 500 pieces of cookies randomly mixed with 1000 nuts including 600 almonds and 400 hazelnuts in which each nut is the same size. Suppose the number of pieces of nuts in a piece of cookie follows a Poisson distribution.

(a) Find the probability that a randomly picked cookie will have no almond.

(b) Find the probability that a randomly chosen cookie will have at least two pieces of nuts in it.

(c) Suppose cookies are randomly selected one-by-one with replacement, find the probability that the fifth chosen cookie will be the 1st cookie without any hazelnut?

(d) Suppose 12 cookies are packed into each box. What is the probability of getting a randomly selected box with at most two pieces of cookies without any nuts?

Reference no: EM132483663

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