In a school, the probability of holding a debate competition is 1/3 and that of a quiz competition is 2/3. In the two participating teams, A has 4…

In a school, the probability of holding a debate competition is $\displaystyle \frac{1}{3}$ and that of a quiz competition is $\displaystyle \frac{2}{3}$. In the two participating teams, A has $\displaystyle 4$ girls and $\displaystyle 6$ boys and B has $\displaystyle 7$ girls and $\displaystyle 3$ 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.