Question

There are $30$ black balls and $40$ white balls in a box. A ball is drawn from the box at random. Find the probability that it is white. If two balls are drawn from the bag find the probability that they are of opposite colours.

Answer 1

Probability that ball is white $=\frac{30}{70}=\frac{3}{7}$

Probability that balls are of opposite colours $=\frac{{}^{40}{C}_1{\times }^{30}{C}_1}{{}^{70}{C}_2}=\frac{40\times 30}{35\times 69}=\frac{80}{161}$