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# Assume that in a family,each child is equally likely to be a boy or a girl.A family with three children is chosen at random.The probability that the eldest child is a girl given that the family has at least one girl is

$\begin{array}{1 1}(A)\;\frac{1}{2}\quad(B)\;\frac{1}{3}\quad(C)\;\frac{2}{3}\quad(D)\;\frac{4}{7}\end{array}$

Can you answer this question?

Toolbox:
• Out of 3 children if at least one is a girl than the sample space contain
• $S(G\;B\;G\;,G\;B\;B\;,G\;G\;G\;,G\;G\;B\;,B\;B\:G\;,B\;G\;B\;,B\;G\;G)$
p(two girls/atleast 1 girl)
=$\frac{4}{7}$
=4 favorable cases in the sample space of 7
'D' is correct choice
answered Feb 21, 2013