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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.

Solution

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

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