Independent random variables

Apricot

2007-01-22 2:18 am

Two phone calls come into a switchboard at random times in a fixed 1-hr period. Assume that the calls are made independently of one another.

What is the probability that the calls are made within 5 min of each other?

回答 (1)

taolo

2007-01-25 9:40 am

✔ 最佳答案

say that 1hrs is 0min to 60min
if call a is in 0min or 60min, the probability that call b made within 5 min is 5/60=1/12
if call a is in between 5min and 55min, the probability that call b made within 5 min is 10/60=1/6
if call a is in between 0min and 5min or in between 55min and 60min, the probability that call b made within 5 min is from 1/12 to 1/6 linearly, so the average probability is (1/12+1/6)/2=1/8
probability that call a made in between 0min and 5min or in between 55min and 60min is 1/6
probability that call a made in between 5min and 55min is 5/6
so probability required = 1/6*1/8+5/6*1/6=23/144

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