Question

From $4$ children, $2$ women and $4$ men, $4$ persons are selected. The probability that there are exactly $2$ children among the selected is

• A. $\frac{7}{3}$
• B. $\frac{3}{7}$
• C. $\frac{2}{7}$
• D. $\frac{2}{9}$

Answer 1

The correct option is B $\frac{3}{7}$

We have $4$ children, $2$ women and $4$ men.

Total $=10$ persons

No $4$ person are selected and there should be exactly $2$ children.

We have Probability, $p=\frac{favourableoutcomes}{totaloutcomes}$

Total outcomes $=$ choosing $4$ person out of $10=$ ${{}^{10}C}_4$

No of favourable outcomes $=$ selection of $2$ children =${{}^{4}C}_2\times {{}^{6}C}_2$

So probablity, $p=\frac{{{}^{4}C}_2\times {{}^{6}C}_2}{{{}^{10}C}_4}=\frac{3}{7}$