Question

A 9th class has 15 boys and 30 girls. Two representatives are to be selected at random from the class. Find the probability for various scenarios.

(i) The first representative is a girl.
(ii) The second representative is a girl, given that the first representative is a boy.
(iii) First is a boy and second is a girl.
(iv) A girl and a boy are selected as representatives.

Answer 1

The probability of different scenarios in selecting representatives from a class with 15 boys and 30 girls pertains to conditional probability and hypergeometric distribution, with calculations based on the total number of students and gender distribution.

Step-by-step explanation:

The question belongs to the domain of probability and involves calculating the probability of various scenarios regarding the selection of class representatives from a 9th class with 15 boys and 30 girls.

Scenario Analysis

1. The probability that the first representative is a girl is 30/45 or 2/3 since there are 30 girls out of a total 45 students.
2. The probability that the second representative is a girl, given that the first representative is a boy, is 30/44 since after selecting a boy, there are 30 girls left out of the remaining 44 students.
3. The probability that the first is a boy and second is a girl is 15/45 * 30/44, since the first draw leaves us with 44 students and the number of girls has not changed.
4. For a girl and boy to be chosen as representatives, we have two ways this can happen: First a girl then a boy, or first a boy then a girl. Therefore, the probability is 30/45 * 15/44 + 15/45 * 30/44 or 1/3.