Teenage drivers pay more for automobile insurance than older drivers. Also, many insurance companies offer discounts for teenage drivers that achieve good grades. Assume that 20% of all teenage drivers are involved in accidents each year. Assume that 10% of all teenage drivers have GPAs that are 3.5 or above. Of the teenage drivers involved in accidents, only 5% of them have GPAs that are 3.5 or above.
a) Let A be the event that a teenager has a GPA of 3.5 or above. Let B be the event that a teenage driver is involved in an accident this year. Find P(A) and P(B).
b) Find P(A given B)
c) Find the probability that a randomly chosen teenage driver has a GPA of 3.5 or above and is involved in an accident this year. (5 points)