A (very bad) factory produces plastic bags such that 30% of the plastic bags produced are defective and 70% are good. A sample of 5 plastic

Question

A (very bad) factory produces plastic bags such that 30% of the plastic bags produced are defective and 70% are good. A sample of 5 plastic bags is selected at random. (a) What is the probability that all 5 bags selected are defective?

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2 hours 2021-09-13T02:41:35+00:00 1 Answer 0

0.24% probability that all 5 bags selected are defective

Step-by-step explanation:

For each bag, there are only two possible outcomes. Either they are defective, or they are not. The probability of a bag being defective is independent from other bags. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

30% of the plastic bags produced are defective

This means that

A sample of 5 plastic bags is selected at random

This means that

What is the probability that all 5 bags selected are defective?

This is P(X = 5). So

0.24% probability that all 5 bags selected are defective