A baker blends 580| raisins into a dough and makes 395| cookies. The probability

Question

A baker blends 580| raisins into a dough and makes 395| cookies. The probability of a raisin being in a randomly picked cookie is 1/395|. Use the Poisson distribution to compute the following probabilities. What is the probability that a randomly picked cookie will have no raisins? What is the probability that a randomly picked cookie will have exactly 1 raisin? What is the probability that a randomly picked cookie will have exactly 3 raisins? What is the probability that a randomly chosen cookie will have at least two raisins in it?

Explanation / Answer

in this question the alpha = 1/395 = 0.0025

formula to be used =

a)p(x=0) = 0.0025^0*(e^(-0.0025)/0! = 0.9975

b)p(x=1) =  0.0025^1*(e^(-0.0025)/1! = 0.0024

c) p(x=3) =  0.0025^3*(e^(-0.0025)/3! = 0.00000001

d) p(x>=2) = 1 -[p(0)+p(1)]

= 1 - 0.9975-0.0024 = 0.0001

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