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A family with three children is chose at random. The probability that the oldest and youngest children are of the same gender is
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$\frac{1}{2}$
$\mathrm{S}=\{\mathrm{BBB}, \mathrm{BBG}, \mathrm{BGB}, \mathrm{BGG}, \mathrm{GBB}, \mathrm{GBG}, \mathrm{GGB}, \mathrm{GGG}\}$
$\mathrm{E}=\{\mathrm{BBB}, \mathrm{BGB}, \mathrm{GBG}, \mathrm{GGG}\}$
$P(\mathrm{E})=\frac{n(\mathrm{E})}{n(\mathrm{~S})}=\frac{4}{8}=\frac{1}{2}$
$\mathrm{E}=\{\mathrm{BBB}, \mathrm{BGB}, \mathrm{GBG}, \mathrm{GGG}\}$
$P(\mathrm{E})=\frac{n(\mathrm{E})}{n(\mathrm{~S})}=\frac{4}{8}=\frac{1}{2}$
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