Question

Three marbles are in a jar—one white, one blue and one green. Two marbles are picked one at a time with replacement. Let X be the number of blue marbles picked. Construct the probability distribution.

Answer 1

Because we replace the first marble before selecting the second, the events are independent, so the probabilities are:

$P(X=0) = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \\ P(X=1) = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9} \\ P(X=2) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$