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# 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 arrives randomly

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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 arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Alex arrives?

Mellie  Apr 24, 2015

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That means the question should probably have been phrased to ask for the probability that Alex catches the train in order to avoid misinterpretation.

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Alan  Apr 26, 2015
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Hi Mellie,

The question is a bit ambiguous so

I am going to assume that the train will arrive on the minute somtime between 1:01 and 1:59 inclusive

Well the train will be there for 10 minutes and alex could arrive anytime in 60 minutes so that would be 1/6

This logic has at least one obvious hole in it. The train could arrive arrive between 1:51 and 1:59 in which case it will not be at the station for a full 10 minutes during the hour.

idk - needs more thought

Melody  Apr 25, 2015
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I should have said the probability that Alex catches the train is given by the area in the red box below and to the right of the blue line divided by the area of the red box.

Alan  Apr 25, 2015
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civonamzuk  Apr 25, 2015
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I interpreted this question as meaning what is the probability that Alex will catch the train.

Strictly interpreted, the question requires the probability that the train is already in the station when Alex arrives, which is how Melody and civonamzuk have interpreted it (in my interpretation Alex could be waiting for some time before the train arrives!).

For the alternative probability I get 11/72 = 0.153.

(On my diagram imagine a line running from (0,0) to (60, 60).  Alex has to arrive in the band between this line and the blue line, the area of which is a fraction 0.153 of the red box area.)

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Alan  Apr 25, 2015
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Hi Alan,

I do not think it is the answer to the question asked

Melody  Apr 26, 2015
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I've given my answer to your (almost certainly correct) interpretation also!  (11/72 or 0.153).

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Alan  Apr 26, 2015
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Melody  Apr 26, 2015
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The answer was 47/72 (what Alan had said before) thanks everybody for your hard work on this question.

Mellie  Apr 26, 2015
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Thanks Mellie :)

Melody  Apr 26, 2015
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