### Question 7

There are 8 boys and 6 girls in a class. If **two** students are selected at random from the class, find the probability that they are of:

- the same sex;
- different sex

### Observation

This question was also reported to be quite popular among the candidates and they performed well in it. Two methods were common among the candidates, the combination method and the product rule of conditional probability. Using the combination method, total number of students = 14. Candidates were expected to obtain the total number of ways of selecting 2 students from 14 students as 14C2 = 91. In part (a), probability of same sex = probability of both boys or both girls = probability of both boys + probability of both girls = + = = or 0.4725.

In part (b), probability of different sex = probability of 1 boy and 1 girl = = = or 0.5275. The probability of different sex can also be gotten by 1 – probability of same sex, since there are only two possibilities- either same sex or different sex. Therefore, probability of different sex = 1 - = or 0.5275.