Question

A brother and a sister are in the same math class. There are 9 boys and 8 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.

The probability is ?

Answer 1

1/72

Explanation:

There are a total of 17 students in the class, and we want to choose one boy from 9 and one girl from 8 without replacement. The total number of ways to choose two students from the class is:

17C2 = (17!)/(2!15!) = (1716)/(21) = 136

To choose a boy and a girl, we can choose the boy in 9 ways and the girl in 8 ways, for a total of 9*8 = 72 ways.

Now, since the brother and sister are both in the class, there is only one way to choose them together. Therefore, the probability of choosing the brother and sister is:

1/72

So the probability is 1/72, written as a fraction in simplest form.