Answer to Question #119446 in Statistics and Probability for desmond

Question

Suppose a ball is drawn at random from a box containing three white and three black
balls. After a ball is drawn, it is then replaced and another drawn. What is the
probability that of the first four balls drawn, exactly two are white?

Answer 1

Probability of first drawn white $= \frac{3C2\times3C2}{6C2} = \frac{3}{5}$

Probability of second drawn white with replacement $= \frac{3C2\times3C2}{6C2} = \frac{3}{5}$

probability of exactly two are white = Probability of first drawn white $\times$ Probability of second drawn white with replacement

probability of exactly two are white $={\frac{3}{5}}\times\frac {3}{5}= \frac {9}{25}$