Question

Two friends are to meet at the library. Each independently and randomly selects an arrival time within the same one-hour period. Each agrees to wait a maximum of fifteen minutes for the other to arrive. What is the probability that they will meet

Answer 1

The probability that they will meet is 0.4375

Explanation:

Let A and B be two friends who choose to meet the same one-hour period.Since there are 60 minutes in an hour therefore n= 60

A can wait for 15 minutes

So the probability of A to meet is given by P(A)= (15/60)= 1/4

Similarly

B can wait for 15 minutes

So the probability of B to meet is given by P(B)= (15/60)= 1/4

The probability that A cannot meet is given by 1- P(A)= 1-1/4= 3/4

Similarly

The probability that B cannot meet is given by 1- P(B)= 1-1/4= 3/4

And

The probability that both A and B cannot meet is given by = 3/4*3/4= 9/16

So the probability that both will meet = 1- 9/16= 7/16= 0.4375