Question

In a group of 20 boys and 10 girls, 5 boys and 3 girls are honest. If two persons are selected at random from the group, find the probability that either both are girls or both are honest. Should there be gender discrimination?

Answer 1

Total number of people in a group $=30$

Total number of honest boys and girls $=8$

If $2$ of them are pick at random then

$P=\frac{{}^5{C}_2{+}^8{C}_2}{{}^{30}{C}_8}=\frac{13}{5852925}$

$\therefore$ Probability that both boys or girls are honest is $\frac{13}{5852925}$ there should be no gender discrimination