Question

a warehouse employs 27 workers on first - shift, 17 workers on second - shift, and 12 workers on third - shift. eight workers are chosen at random to be interviewed about the work environment. find the probability of choosing exactly five first - shift workers. the probability of choosing exactly five first - shift workers is (round to three decimal places as needed.)

Explanation:

Step1: Calculate total number of workers

The total number of workers is \(27 + 17+12 + 8=64\) workers.

Step2: Use combination formula for probability

The number of ways to choose 8 workers out of 64 is \(C(64,8)=\frac{64!}{8!(64 - 8)!}\). The number of ways to choose 5 first - shift workers out of 27 first - shift workers and \(8 - 5=3\) non - first - shift workers out of \(64 - 27 = 37\) non - first - shift workers is \(C(27,5)\times C(37,3)=\frac{27!}{5!(27 - 5)!}\times\frac{37!}{3!(37 - 3)!}\).

Step3: Calculate the probability

The probability \(P=\frac{C(27,5)\times C(37,3)}{C(64,8)}\)

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Answer:

0.014