Question

127 cars were sold during the month of april. 74 had air conditioning and 59 had automatic transmission. 58 had air conditioning only, 43 had automatic transmission only, and 10 had neither of these extras. what is the probability that a randomly selected car had automatic transmission or air conditioning or both?

Answer 1

To calculate the probability that a randomly selected car had automatic transmission or air conditioning or both, we can use the inclusion-exclusion principle.

Step-by-step explanation:

To calculate the probability that a randomly selected car had automatic transmission or air conditioning or both, we can use the inclusion-exclusion principle.

We know that 74 cars had air conditioning and 59 cars had automatic transmission. 58 cars had air conditioning only, 43 cars had automatic transmission only, and 10 cars had neither extras.

To find the total number of cars with either automatic transmission or air conditioning or both, we can sum the number of cars with each individual option and subtract the number of cars with both options.

So, the probability is:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = (74/127) + (59/127) - (43/127)

P(A or B) = 0.582