11. (5 points) Painting bears

Suppose that, at the start of the day, a jar contains a random number of bears that has a Poisson distribution with mean 18. During the day, each such bear is randomly painted red, blue, or yellow, with each of these three possibilities being equally likely, and with the painting of bears being independent. Suppose that, at the end of the day, we discover that there are 7 red bears and 3 blue bears.

(a) (3 points) Given all of the information above, what kind of random variable is the number of yellow bears at the end of the day?

(b) (2 points) How many yellow bears do we expect?