Question

among sixteen new machines that were sold to a distributor. There are seven with minimum defects....

among sixteen new machines that were sold to a distributor. There are seven with minimum defects. If the quality control department randomly selects two of these machines to check for defects, what is the probability that: a) none of the machines have defects, b) one of the machines has defects

Math   Statistics-And-Probability   
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Answer #1

We use Binomial distribution to solve this problem.

Probability mass function of binomial distribution is :

where,

n = Number of trials

p = Probability of success

x = Number of success

a)

Probability that none of the machines have defects = P(X=0)

In this case,

n = Number of machines selected = 2

p = Probability of defects = 7 / 16 = 0.4375

Probability that none of the machines have defects = 0.3164

b)

Probability that one of the machines has defects = P(X=1)

Probability that one of the machines has defects = 0.4922

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