Fun with Hypergeometric Probabilities: A floor broker has a new assistant that p

Question

Fun with Hypergeometric Probabilities: A floor broker has a new assistant that processes 100 orders per hour. Based upon past experience, there are 3 orders (out of 100) that have slight input errors by an assistant. A sample of 12 orders is chosen at random, and it is found that there are 2 errors in the sample.

Use the hypergeometric distribution to calculate the probability of having 2 errors in the sample of 12.

a. What is the probability of having 0 or 1 errors in a sample of 12?

b. What is the probability of having more than 2 errors in a sample of 12?

c. Given your answer in part (c), how do you think of the assistant’s job performance?

Explanation / Answer

a) P(having 2 errors) = P(X = 2) =   3C2 * 97C10/100C12 = 0.036

b) P(having 0 or 1 error ) = (3C0 * 97C12 + 3C1 * 97C11)/100C12 = 0.963

c) P(more than two error) = P(X > 2) = P(X = 3)

                                                          = 3C3 * 97C9 /100C12 = 0.001

d) As the probability is less than 0.05 (0.001 < 0.05), so it is unusal

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