The owner of an auto dealership believes that the number of cars they sell every week can be described by a Poisson probability model. The owner believes that in a "good" week the average number of cars they sell is 10 and in a "bad" week the average number of cars they sell is 5.

(a) What is the probability that exactly 6 cars will be sold in a good week? What is the probability that exactly 6 cars will be sold in a bad week?

(b) The owner believes that 70 % of the weeks are good weeks (and 30 % are bad weeks). Given this information, what is the probability that exactly 6 cars will be sold in any week?

(c) Given that the dealership sold 6 cars last week, what is the prob- ability that they had a good week ?

(d) Given that the dealership sold less than 6 cars last week, what is the probability that they had a bad week?