Question

A small class has

10
students,
6
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 boy and the second will be a girl? Write your answer as a fraction in simplest form.

Answer 1

6/10=3/5 girls
4/10=2/5 boys

Answer 2

`P = (2)/(5)*(2)/(3) = (4)/(15)`

Explanation:

The are no replacements.

For the selection of the first student, there are 10 students, 4 of which are boys. So there is a 4/10 = 2/5 probability that the first student chosen is a boy.

Now, for the second student. There are 9 students, of which 6 are girls. So there is a 6/9 = 2/3 probability that the second will be a girl when the first was a boy.

So

`P = (2)/(5)*(2)/(3) = (4)/(15)`