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?

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

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