Question

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.

Answer 1

\[\text{ Given : Box } = \left( 10B + 8R \right) \text{ balls } \]

\[ P\left( \text{ one is red and one is black } \right) = P\left( \text{ first red and second black } \right) + P\left( \text{ first red and second black } \right)\]
\[ = \frac{8}{'18} \times \frac{10}{18} + \frac{10}{18} \times \frac{8}{18}\]
\[ = \frac{80}{324} + \frac{80}{324}\]
\[ = \frac{40}{81}\]