Question

In a class of 10, there are 2 students who forgot their lunch. If the teacher chooses 2 students, what is the probability that both of them forgot their lunch?

Answer 1

At the beginning, the chances that the teacher will choose a student who has forgotten his lunch are 2/10, or 1/5.

If the teacher now chooses another student from the remaining 9 students, the chances of his choosing a student who has forgotten his lunch are 1/9, since one of the forgetful students has already been removed from the original group of 10 students, and there are only 9 in the group remaining.

The probability that both students forgot lunch is (1/5)(1/9), or 1/45.