A multinational business unit has an examination system for the batches of ventilator units bought from dealers. A batch typically comprises 80 ventilators. In the inspection system, a random sample of 20 is selected and all are tested. Suppose there are 6 faulty ventilators in the batch of 80. What is the probability that for a given sample there will be less than 3 faulty ventilator?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A multinational business unit has an examination system for the batches of ventilator units bought from dealers. A batch typically comprises 80 ventilators. In the inspection system, a random sample of 20 is selected and all are tested. Suppose there are 6 faulty ventilators in the batch of 80. What is the probability that for a given sample there will be less than 3 faulty ventilator?

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Step 1

The binomial probability distribution is,

PX=x=nxpx1-pn-x

In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.

The random variable X is defined as the number of faulty ventilators which follows binomial distribution with sample size 20 and probability of success 0.075=680.

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