Question

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

Answer 1

Probability of first drawn white $= \frac{3C2\times3C2}{6C4} = \frac{3}{5}$

Probability of second drawn white with replacement $= \frac{3C2\times3C2}{6C4} = \frac{3}{5}$

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 $={\frac{3}{5}}\times\frac {3}{5}= \frac {9}{25}$