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# probability

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John needs to catch a train. The train arrives randomly some time between 2:00 and 3:00, waits for 15 minutes, and then leaves. If John also arrives randomly between 2:00 and 3:00, what is the probability that the train will be there when John arrives?

Dec 26, 2020

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John has a $$100$$% chance of being there if he arrives at $$2:20$$ or earlier. Add $$\frac13$$.

At $$3:00$$, he has a $$\frac13$$ chance. We can take this and take the average from $$2:20$$ and $$3:00$$ to get $$\frac23$$ for this $$40$$ minute period. Multiply this by the portion of time. Add $$\frac49$$ to the probability.
Result: He has a $$\frac79$$ chance of catching the train.

Credit to helperid1839321; https://web2.0calc.com/questions/john-needs-to-catch-a-train#r1

P.S. I changed up helperid1839321's answer a little, so please give me a little credit also!

Dec 28, 2020
edited by cryptoaops  Dec 28, 2020