20 of people are accidentprone and have a probability 015 of

20% of people are “accident-prone” and have a probability 0.15 of having an accident in a 1-year period in contrast to a probability of 0.05 for the other 80% of people. (a) If we pick a person at random, what is the probability that they will have an accident this year? (b)What is the probability a person is accident-prone if they had an accident last year? (c) What is the probability that they will have an accident this year if they had one last year?

Solution

a)

0.15*0.20 = 0.03

b)

0.80 * 0.05 = 0.04

c)

0.03 / 0.04 = 0.75