Question

Assume that each child born is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:
1. 1/11
2. 1/10
3. 1/12
4. 1/17

Answer 1

Correct Answer - Option 1 : 1/11

From question, the probability of getting at least two girls among four children is:

\(G\;G\;G\;G \to {}_\;^4{C_4} = \frac{{4 \times 3 \times 2 \times 1}}{{1 \times 2 \times 3 \times 4}} = 1\)

\(G\;G\;G\;B \to {}_\;^4{C_3} = \frac{{4 \times 3 \times 2}}{{1 \times 2 \times 3}} = 4\)

\(G\;G\;B\;B \to {}_\;^4{C_2} = \frac{{4 \times 3}}{{1 \times 2}} = 6\)

Now, the required probability is given by the formula:

Probability of an Event \(= \frac{{{\rm{\;Number\;of\;Favorable\;Outcomes\;}}}}{{{\rm{\;Total\;Number\;of\;Possible\;Outcomes\;}}}}\)

Now, substituting the values,

⇒ Probability of an Event \(= \frac{1}{{1 + 4 + 6}}\)

∴ Probability of an Event = 1/11