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Two balls are...

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 another is red.

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Solution

Consider the following events:
Total number of balls= $18$
Total number black balls= $10$
Total number of red balls= $8$
Probability of a ball drawn is black = $\frac{10}{18}$
Probability of a ball drawn is red = $\frac{8}{18}$

Required probability

$\Rightarrow \frac{8}{18} \times \frac{10}{18} + \frac{10}{81} \times \frac{8}{81}$

$= \frac{40}{81}$

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