From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. What is the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

0.6864 = 68.64% probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

Step-by-step explanation:

The cars are chosen without replacement, so the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

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

In which:

x is the number of sucesses.

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.

48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.

This means that

8 cars received.

This means that

What is the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios

This is

In which

0.6864 = 68.64% probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios