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John needs to catch a train. The train arrives randomly some time between 2:00 and 3:00, waits for 20 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?

 Sep 3, 2018
 #1
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John has a 100% chance of being there if he arrives at 2:20 or earlier. Add 1/3.

At 3:00, he has a 1/3 chance. We can take this and take the average from 2:20 and 3:00 to get 2/3 for this 40 minute period. Multiply this by the portion of time. Add 4/9 to the probability.
Result: He has a 7/9 chance of catching the train.

 Sep 5, 2018
 #2
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See Alan's answer No.#2 here. Make sure to adjust for the time difference of 20 minutes instead of 10 minutes in this particular question: p=1 - (1/2(60 - 20)^2/60^2 =(1/2*40^2)/60^2 =1 - 2/9 =7/9:

https://web2.0calc.com/questions/alex-needs-to-catch-a-train-the-train-arrives-randomly-some-time-between-1-00-and-2-00-waits-for-10-minutes-and-then-leaves-if-alex-also

 Sep 5, 2018

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