Question

In a school, the probability of holding a debate competition is $\frac{1}{3}$ and that of a quiz competition is $\frac{2}{3}$. In the two participating teams, A has 4 girls and 6 boys and B has 7 girls and 3 boys. If a debate competition is held, the students are selected from team A and for the quiz competition they are selected from team B. If only two students are to be chosen from the teams, then find the probability that one will be a girl and the other a boy.

Hint:

Keep the denominators common ($\frac{135}{}$) throughout your intermediate calculations instead of simplifying $P(E|D)$ and $P(E|Q)$ too early. This will make adding fractions at the end much simpler.

Answer 1