Question 42

A bag contains 24 eggs out of which 8 are rotten. The remaining eggs are not rotten eggs. The two eggs are selected at random, What is the probability that one of the eggs is rotten?

Number of rotten eggs = 8
Number of non-rotten eggs = 16
Required probability = $$\frac{^8C_1 . ^{16}C_1}{^{24}C_2} + \frac{^8C_2}{^{24}C_2}$$
= $$\frac{8 \times 16 + 28}{276}$$
= $$\frac{13}{23}$$

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