Question

Suppose that a drawer contains 8 marbles: 2 are red, 2 are blue, 2 are green, and 2 are yellow. The marbles are rolling around in a drawer, so that all possibilities are equally likely when they are drawn. Alice chooses 2 marbles without replacement, and then Bob also chooses 2 marbles without replacement. Let Y denote the number of red marbles that Alice gets, and let X denote the number of red marbles that Bob gets.

8a. Find E(X | Y=0).

8b. Find E(X | Y=1).

8c. Find E(X | Y=2).

Answer 1

Y denotes the number of red marbles that Alice gets.

X denotes the number of red marbles that Bob gets.

There is a total of8 ball, 2 red balls and 6 not red balls

a) P(X=0 | Y =0) = This means the conditional probability that X=0 given Y =0. Y=0 means Alice did not get any red marble

b)

c)