Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. proba

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14.Probability

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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.

A

$\frac{16}{81}$

B

$\frac{16}{81}$

C

$\frac{16}{81}$

D

$\frac{16}{81}$

Solution

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 $=\frac{4}{9} \times \frac{4}{9}=\frac{16}{81}$

Standard 11

Mathematics

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(IIT-1988)