# Aptitude | GATE CS 1998 | Question 56

[Subjective type]

Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 p.m. and 5:00 p.m. and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave.  What is the probability that the two will not meet?

Explanation: Let us consider two friends to be A and B

probability that A comes between 4:00p.m and 4:50pm and B comes in the next 10 mins is (5/6)*(1/6)

probability that B comes between 4:00p.m and 4:50pm and A comes in the next 10 mins is (5/6)*(1/6)

probability that both A and B comes in the last 10 mins is (1/6)*(1/6)

probability that the both meet is (5/6)*(1/6)+(5/6)*(1/6)+(1/6)*(1/6)=11/36

probability that they will not meet = 1-p(they will meet)=1-11/36=25/36

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