Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that both balls are red.
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that both balls are red.
Total number of balls $=18$
Number of red balls $=8$
Number of black balls $=10$
Probability of getting a red ball in the first draw $=\frac{8}{18}=\frac{4}{9}$
The ball is replaced after the first draw.
$\therefore$ Probability of getting a red ball in the second draw $=\frac{8}{18}=\frac{4}{9}$
Therefore, probability of getting both the balls red $=\frac{4}{9} \times \frac{4}{9}=\frac{16}{81}$
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