A batch of 10 discs has 3 defective discs. A sample of 5 discs is randomly...

A batch of 10 discs has 3 defective discs. A sample of 5 discs is randomly selected from the batch.

A. Find the probability that exactly one disc in the sample is defective.

B. Find the probability that at least 4 discs in the sample are not defective.

Expert Solution

This is a hypergeometric distribution.

N = 10

k = 3

n = 5

a) P(X = 1) = 3C1 * 7C4 / 10C5 = 3 * 35 / 252 = 0.4167

b) P(at least 4 not defective) = P(at most 1 is defective)

= P(X < 1)

= P(X = 0) + P(X = 1)

= [3C0 * 7C5 / 10C5] + [3C1 * 7C4 / 10C5]

= 0.5

orchestra answered 1 year ago

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