A warehouse contains ten printing machines, two of which are defective. A company selects seven of the machines at random, thinking all are in working condition. What is the probability that all seven machines are nondefective?

0.0667 = 6.67% probability that all seven machines are nondefective.

Step-by-step explanation:

The machines 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:

10 machines means that

2 defective, so 10 - 2 = 8 work correctly, which means that

Seven are selected, which means that

What is the probability that all seven machines are nondefective?

This is P(X = 7). So

0.0667 = 6.67% probability that all seven machines are nondefective.

step-by-step explanation: s