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# An Uncertain Meeting

7 replies to this topic

### #1 ujjagrawal

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Posted 16 August 2012 - 08:59 AM

There are two friends, who decide to meet at a place between 5 PM to 6 PM everyday. What are the chances that, on a given day, they will be able to meet. Provided-

Case 1: They agreed whoever comes first, will wait for 15 minutes for another friend to arrive.
Case 2: One friend wait for 10 minutes and other for 20 minutes for another friend to arrive.

And which of the above two cases holds better chances of there meeting ?

Edited by ujjagrawal, 16 August 2012 - 09:00 AM.

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### #2 jim

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Posted 16 August 2012 - 04:40 PM

You can answer this question if you solve a single problem: What is the probability of meeting if one friend waits 15 + x minutes and the other waits 15 - x minutes?
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### #3 bushindo

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Posted 17 August 2012 - 01:10 AM

There are two friends, who decide to meet at a place between 5 PM to 6 PM everyday. What are the chances that, on a given day, they will be able to meet. Provided-

Case 1: They agreed whoever comes first, will wait for 15 minutes for another friend to arrive.
Case 2: One friend wait for 10 minutes and other for 20 minutes for another friend to arrive.

And which of the above two cases holds better chances of there meeting ?

Assuming the arrival time for the two friends are independently, identically, and uniformly distributed over the hour, then
Spoiler for comparison

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### #4 bonanova

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Posted 17 August 2012 - 03:54 AM

Spoiler for I get

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #5 ujjagrawal

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Posted 17 August 2012 - 05:27 AM

Assuming the arrival time for the two friends are independently, identically, and uniformly distributed over the hour, then

Spoiler for comparison

I had got the same answers as you... but would like to see how you had worked it out...
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### #6 bushindo

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Posted 17 August 2012 - 06:08 AM

I had got the same answers as you... but would like to see how you had worked it out...

Here's the integral I used for Case 1,
Spoiler for integral

I like bonanova's approach much better though.
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### #7 Chavers

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Posted 20 August 2012 - 03:32 AM

Neither would show up at 5:00 since they both can wait 15 minutes. Neither would show at 5:15 since they each would expect the other to show at that time. Ether they both will arrive 5:30 or meet at 5:45 since they would both expect 6:00 to be too late.
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### #8 ujjagrawal

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Posted 21 August 2012 - 01:05 PM

Here's the integral I used for Case 1,

Spoiler for integral

I like bonanova's approach much better though.

My workings
Spoiler for My solution for the same

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