Among 15 metal parts produced in a machine shop 3 are defect

Among 15 metal parts produced in a machine shop, 3 are defective. If a random sample of 8 of these metal parts is selected, find

The probability that this sample will contain at least two defectives. (Do not round the intermediate answers. Round your answer to 4 decimal places.)

The probability that this sample will contain at most one defective. (Round your answer to 4 decimal places.)

Solution

a)

Note that

P(at least 2 defective) = 1 - P(at most 1 defective)

There are 15C8 ways to choose any eight, and there are (12C8) ways to choose all non defective, and (12C7)*3 ways to choose one defective.

Thus,

P(at most 1 defective) = [12C8 + (12C7)*3]/(15C8) = 0.446153846

Thus,

P(at least 2 defective) = 1 - P(at most 1 defective)

= 0.553846154 [ANSWER]

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b)

As said in part a,

P(at most 1 defective) = [12C8 + (12C7)*3]/(15C8) = 0.446153846 [ANSWER]