Binomial or Poission Probabilities:A baker put 700 raisins into dough, mixed well, and made 100 cookies....

Binomial or Poission Probabilities:A baker put 700 raisins into dough, mixed well, and made 100 cookies. You take a random cookie. What is the probability of finding at least five raisins in it?

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Expert Solution

Here, we use approximation to the Binomial distribution of the number of taisins in one cookie

The number of raisins X in one cookie is Binomial with n = 700 and p = 1/100 = 0.01, it is approximately Poisson with parameter np = 700*0.01 = 7. The proabability of finding at lest five raisins is

P(X 5) = 1 - P(X<5)

Poisson distribution:

...................X = 0,1,2,3,.......................

Where, Mean = = np = 700*0.01 = 7

P(X 5) = 1 - P(X<5)

P(X 5) = 1 - P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X 5) = 1 - 0.1730

P(X 5) = 0.8270

From the poisson table

orchestra answered 1 year ago

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