Question

136 cars were sold during the month of april. 78 had air conditioning and 68 had automatic transmission. 56 had air conditioning only, 46 had automatic transmission only, and 12 had neither of these extras. what is the probability that a randomly selected car had automatic transmission or air conditioning or both?

Answer 1

Let us see how many cars had both of these 2 extras; since there were 78 cars with air conditioning and 56 with airconditioning only, we get that there were 22 cars with both of these features (automatic transmission/ air conditioning). If we add the cars that had only AC and the cars that had only AT, as well as the cars that had both, we get all the cars that satisfy the described event. This is equal to 56+46+22=124. Thus, the probability is given by 124/136=91.2%.
We could also claim that since 12 of the cars do not have any of the features, any of the remaining 136-12 cars would have at least one feature; hence the probability would be given by (136-12)/136 and we have obviously the same result.