Question

Consider 5 fish in a bowl: 3 of them are red, and 1 is green, and 1 is blue. Select the fish one at a time, without replacement, until the bowl is empty.

Let X=1 if all of the red fish are selected, before the green fish is selected; and X=0 otherwise.

Let Y=1 if all of the red fish are selected, before the blue fish is selected; and Y=0 otherwise.

a. Find the joint probability mass function of X and Y.

pX,Y(0,0)=

pX,Y(0,1)=

pX,Y(1,0)=

pX,Y(1,1)=

b. Make sure that the four probabilities pX,Y(0,0), pX,Y(0,1), pX,Y(1,0), and pX,Y(1,1) from part 3a have a sum of 1.

c. Find the probability pX(1). Find the probability pY(1).

pX(1)=

pY(1)=

d. Are X and Y independent?

Answer 1