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Makky07
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A train station is served by express tains which run every 05 Mar 2004, 08:54
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A train station is served by express tains which run every hour at 10 mins past the hour, and local trains which run every quarter of an hour, starting at 5 past the hour. What is the probability that a passenger arriving at the station at random will have to wait more than six minutes for a train?

Please include your reasoning.

Thanks



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A train station is served by express tains which run every 05 Mar 2004, 09:04
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Is it 31/60

If so, explanation will follow.
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Makky07
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A train station is served by express tains which run every 05 Mar 2004, 09:22
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Yes, the answer is 31/60 although I got 33/60. Can you please explain?
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kpadma
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A train station is served by express tains which run every 05 Mar 2004, 09:30
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ndidi204
Yes, the answer is 31/60 although I got 33/60. Can you please explain?


It may be better for you, if I point out the mistake that you made.
Could you post the your steps.

I'll post mine, if it is different.
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mantha
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A train station is served by express tains which run every 05 Mar 2004, 09:38
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31/60 seems correct.

Draw an hour line with markers at 5, 10, 20, 35 and 50 and you will see that 4+9+9+9 out of 60 mintues one will be 6 min or more waiting.
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A train station is served by express tains which run every 05 Mar 2004, 09:39
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I just looked it over and realized I miscounted.

This is what I did. I picked a 60 mins time frame say 1:05pm to 2:05pm.

From 1:05 to 1:20, the maximum wait over 6 mins is 4 mins
From 1:20 to 1:35, the maximum wait over 6 mins is 9 mins
From 1:35 to 1:50, the maximum wait over 6 mins is 9 mins
From 1:50 to 2:05, the maximum wait over 6 mins is 9 mins

9+9+9+4 = 31 out of 60 mins time frame

My previous mistake was counting 11 mins instead of 9 mins maximum wait in one of the above segments.

Is there a shorter way to figure this out?
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A train station is served by express tains which run every 05 Mar 2004, 09:58
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ndidi204
I just looked it over and realized I miscounted.
Is there a shorter way to figure this out?

Yes, That is the method!



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