Answer
$\frac{1}{16}$
Work Step by Step
List the probabilities for each step:
1. one white: $p(1)=\frac{1}{2}$
2. two whites: $p(2)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$
3. two whites, one black: $p(3)=\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}$, one black added
4. two whites, two blacks: $p(4)=\frac{1}{8}\times\frac{2}{3}=\frac{1}{12}$, one black added
5. two whites, three blacks: $p(5)=\frac{1}{12}\times\frac{3}{4}=\frac{1}{16}$
