The quality assurance engineer of a receiving-sets manufacturer inspects receiving-sets in lots of 50. He selects 4 of the 50 receiving-sets at random and inspects them thoroughly. Assuming that 5 of the 50 receiving-sets in the current lot are defective, find the probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

Step-by-step explanation:

Sets are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

In this question:

Lots of 50 means that

5 are defective, which means that

4 are selected, which means that

Find the probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

This is . So

0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

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