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Question

# Sid is sitting at a bus stop, noting down the time interval of the buses arriving at the stop. His readings are as follows: Bus123456789101112131415Time(hr:min)8:158:188:238:298:328:408:458:528:549:009:079:139:209:259:32 What is the probability that the next bus will come within 5 minutes?(in decimals) __

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Solution

## The time interval between each bus is as follows: Bus123456789101112131415Time(hr:min)8:158:188:238:298:328:408:458:528:549:009:079:139:209:259:32Time Interval(in min)−35638572674757 So, the number of buses that arrived within 5 minutes is = 7 Therefore the probability that the next bus will come within 5 minutes is =714=12=0.5. Note: We do not consider 15 buses in this case because Sid does not know when the last bus before 8:15 was. Hence he cannot say the exact time interval for the first bus.

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