In the MBA Programme of a B - School, there are two sections A and B. 1/4th of the students in Section A and 4/9th of the students in section B are girls. If two students are chosen at random, one each from section A and Section B as class representative, the probability that exactly one of the students chosen is a girl, is :

Probability of choosing a boy from Section A = 3/4

Probability of choosing a boy from Section B = 5/9

Probability of choosing a girl from Section A = 1/4

Probability of choosing a girl from Section B = 4/9

There are two cases. 

Case 1: Boy from section A and girl from section B

Probabilty = $$\frac{3}{4}$$ x $$\frac{4}{9}$$

Case 2: Boy from section A and girl from section B

Probabilty = $$\frac{1}{4}$$ x $$\frac{5}{9}$$

Adding gives final probability = $$\frac{12}{36}$$ + $$\frac{5}{36}$$ = $$\frac{17}{36}$$