Question

118 cars were sold during the month of April. 68 had air conditioning and 61 had automatic transmission. 44 had air conditioning only, 37 had automatic transmission only, and 13 had neither of these extras. What is the probability that a randomly selected car had automatic transmission or air conditioning or both?

Answer 1

88.98% probability that a randomly selected car had automatic transmission or air conditioning or both

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

37 had automatic transmission only

44 had air conditioning only

61 had automatic transmission

This already counts those with both automatic transmission and air conditioning. So 61-37 = 24 had both.

So
`D = 37 + 44 + 24 = 105`

Total outcomes:

118 cars sold, so
`T = 118`.

What is the probability that a randomly selected car had automatic transmission or air conditioning or both?

`p = (D)/(T) = (105)/(118) = 0.8898`

88.98% probability that a randomly selected car had automatic transmission or air conditioning or both