Question

Mark the correct alternative in each of the following:

In a family of 3 children, the probability of having at least one boy is

(a) $\frac{7}{8}$ (b) $\frac{1}{8}$ (c) $\frac{5}{8}$ (d) $\frac{3}{4}$ [CBSE 2014]

Answer 1

The possible outcomes are BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.

∴ Total number of outcomes = 8

The favourable outcomes are BBB, BBG, BGB, GBB, BGG, GBG, GGB.

So, the favourable number of outcomes are 7.

∴ P(at least one boy) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{7}{8}$

Hence, the correct answer is option A.