elevator has 4 passengers and stops at 7 floors. equally likely person will get off at any of the 7 stops. probability that two people get off at the same stop?

Answer 1

What is the probability that any person will exit on the next stop?

We'll figure it this way:

Starting at the 1st floor, the probability that any one person exists the next floor is 1/6

The probability is then 1/6 * 1/6 = 1/36

If that does not happen, the probability then increases to 1/5*1/5 = 1/25

If that does not happen, the probability the increase to 1/4*1/4 = 1/16

5th floor shall be 1/3*1/3 = 1/9

6th floor shall be 1/2*1/2 = 1/4

By the 7th, it is guaranteed to happen as 1/1*1/1= 1/1 = 1 = 100%