First slide

Theorems of probability

Question

Three groups of children contain 3 girls and 1 boy, 2 girls and 2 boys, 1 girl and 3 boys respectively. One child is selected at random from each group. The chance that the selected group comprises of 1 girl and 2 boys is

Moderate

A

$\frac{13}{32}$
B

$\frac{16}{32}$
C

$\frac{19}{32}$
D

$\frac{3}{12}$

Solution

$(G B B) + (B G B) + (B B G)$
$P (E) = \frac{3}{4} . \frac{2}{4} . \frac{3}{4} + \frac{1}{4} . \frac{2}{4} . \frac{3}{4} + \frac{1}{4} . \frac{2}{4} . \frac{1}{4} = \frac{13}{32}$

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