task with pousson distribution
I am stuck on one task:
An insurance company divides its customers into 2 groups. Twenty percent
of customers are in the high-risk group, and eighty percent are in the low-risk
group. The high-risk customers make an average of 1 accident per year while
the low-risk customers make an average of 0.1 accidents per year. Mr. X had
no accidents last year. What is the probability that he is a high-risk driver?
I made something like this:
A - event Mr. X is high-risk driver
B - event Mr. X is low-risk driver
Y - random variable of number of times Mr.X had accidents last year.
By Poisson I got
P (Y=0 | A ) = 0,368 (lambda=1)
P(Y=0 | B ) = 0,905 (lambda=0.1)
So I guess I need to find
P(A | Y=0) = ? or maybe P (A ) = ?
There are two more parameters 0.2 probability of being high-risk driver and 0.8 probability of being low-risk driver.
Thanks in advance.