Question

Three groups of children contain 3 girls and one boy, 2 girls and 2 boys, one girl and 3 boys. One child is selected at random form each group. What is the chance that the three selected consist of 1 girl and 2 boys?

• A. $\frac{17}{32}$
• B. $\frac{11}{32}$
• C. $\frac{3}{32}$
• D. $\frac{13}{32}$

Answer 1

The correct option is D

$\frac{13}{32}$

Selection can be made in the following manner:
(i) Boy, boy, girl
Probability $p_1=\frac{1}{4}.\frac{2}{4}.\frac{1}{4}=\frac{1}{32}$

(ii) Boy, girl, boy
Probability $p_2=\frac{1}{}4.\frac{2}{4}.\frac{3}{4}=\frac{3}{32}.$

(iii) Girl, boy, boy,
Probability $p_3=\frac{3}{4}.\frac{2}{4}.\frac{3}{4}=\frac{9}{32}.$

Since these are mutually exclusive cases, probability
$=p_1+p_2+p_3=\frac{13}{32}$