Posted by **sarah** on Saturday, July 6, 2013 at 1:25am.

For a family with 2 children, the sample space indicating boy (B) or girl (G) is BB, BG, GB, and GG. If each of the outcomes is equally likely, find the probability that the family has 2 girls, given that the first child is a girl.

- probability -
**MathMate**, Saturday, July 6, 2013 at 6:31am
This is a problem of conditional probability. The shortcut to the answer is consider only the outcomes where the first child is a girl, and calculate the probability among those where both are girls.

I.E.

Ω={GG,GB}

favourable outcome: {GG}

So assuming all outcomes are equally probable, then

P(GG|first child is a girl)=1/2

The proper way is to use the definition:

P(GG|GX) ...both girls given first child is a girl

=P(GG∩GX)/P(GX)

=P(GG)/P(GX) .. since P(GG&GX)=P(GG) by absorption

=(1/4)/(1/2)

=1/2

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