A school supply closet contains a box of 21 AA batteries. After testing the batteries, only 10 of them worked. What is the probability of selecting a battery that works followed by a battery that doesn't work without replacing the first?

Question

A school supply closet contains a box of 21 AA batteries.  After testing the batteries, only 10 of them worked.  What is the probability of selecting a battery that works followed by a battery that doesn't work without replacing the first?

mathstudent55 · Answer

The first selection, you are looking for 1 of 10 in 21 so the probability of getting a working battery is 10/21.
After the first selection, without replacement, there will be 20 batteries left with only 9 working and 11 non-working batteries, so the probability of selecting a non-working battery the second time is 11/20.
The overall probability then is 10/21 * 11/20