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Question

A bus comes to a station once every 10 minutes and waits at the station for 1.5 minutes. Find the probability that the bus will be at the station when you arrive.

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If a bus is arriving every 1010 minutes, then it is coming for 6010=6\dfrac{60}{10}=6 times every hour. Each time it stays for 1.51.5 minutes so this makes a total of 6×1.5=96\times1.5=9 minutes. Therefore, every hour, there are 99 minutes to find the bus, so its probability is 960=320\dfrac{9}{60}=\dfrac{3}{20}.

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