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Question
A and B decide to meet at Hanuman temple between 5 pm and 6 pm with a condition that no one would wait for other more than 15 minutes. What is the probability that they meet?
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Solution
If A arrives before B, then the probability that he arrives during first 3/4hour is 3/4.
He'll then wait for 1/4hours.
He arrives during the last 1/4hours, with proability 1/4.
He then waits for 1/8hour on average. Thus his total wait time is 3/4∗1/4+1/4∗1/8=7/32.
For A and B to meet, B must arrive when A is waiting.
Thus the probability that B arrived when A was waiting is 7/32.
Similarly if B arrives before A, the probability that they meet is 7/32.
Thus, Total probability that they meet is 7/16
He'll then wait for 1/4hours.
He arrives during the last 1/4hours, with proability 1/4.
He then waits for 1/8hour on average. Thus his total wait time is 3/4∗1/4+1/4∗1/8=7/32.
For A and B to meet, B must arrive when A is waiting.
Thus the probability that B arrived when A was waiting is 7/32.
Similarly if B arrives before A, the probability that they meet is 7/32.
Thus, Total probability that they meet is 7/16
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