An actuary studied the likelihood that different types of drivers have at least one collision during any one-year period. The results of the study appear below.

Question

TypePercentageCollision %
teen	13	15
young adult	15	5
middle aged adult	43	2
senior	29	9

Find the probability that a driver with at least one collision in the past year is a middle aged adult driver.

Answer 1

Studying for P/1?

One way to approach this problem: you start with some large number of people, pick a number such that all your numbers end up being whole numbers. In this case, 10,000 people.

1300 are teens. They get in 195 accidents

1500 are young adults. They get in 75 accidents

4300 are middle aged. They get in 86 accidents.

2900 are seniors. They get in 261 accidents.

So our denominator is (people who got in accidents) which is 195+75+86+261 = 617.

Our numerator is (people who are middle aged who got in an accident) which is 86.

So your answer is 86/617 = 13.94%

You can do this all with just percentages, but I find that using whole numbers makes it all clearer.