Question

A small class has

9
students,
5
of whom are girls and
4
of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a girl and the second will be a boy? Write your answer as a fraction in simplest form.

Answer 1

1 out of 9 because the teacher will either choose one girl or boy

Answer 2

`(5)/(18)` is the probability that the first student chosen will be a girl and the second will be a boy.

Explanation:

we are given the following information in the question:

Total number of students in a class = 9

Total number of girls in a class = 5

Total number of boys in a class = 4

We have to find the probability that the first student chosen will be a girl and the second will be a boy.

Formula:

`\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}`

`\text{P(first student chosen will be a girl and the second will be a boy)}=\\\text{P(first student chosen will be a girl)}* \text{P(second student chosen will be a will be a boy)}`

Working:

`\text{P(first student chosen will be a girl)} = \displaystyle(5)/(9)\\\\\text{P(second student chosen will be a boy)} = \displaystyle(4)/(8)\\\\`

`\text{P(first student chosen will be a girl and the second will be a boy)}= \displaystyle(5)/(9)* (4)/(8)\\\\(20)/(72) = (5)/(18)`

Hence,
`(5)/(18)` is the probability that the first student chosen will be a girl and the second will be a boy.