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probability - unknown source

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by agni_mba » Sat Oct 20, 2007 1:13 pm
Two persons agree to meet at between 2 PM to 4 PM, but each of them will wait 30 minutes for the late comer. What is the probability that they will meet?

Can someone please give an approach?

thanks
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by jangojess » Sat Oct 20, 2007 10:26 pm
this what i think can be the ans...
probability that both can meet = probability that both come b/w 2 PM and 4:30 PM in a day at a particular time. here 4:30 PM is taken because a person can wait for 30 mins for late comer

prob that a person will come at a place b/w 2 and 4:30 PM in a day = 2.5/24 = 5/48

So reqd prob = (5/48) ^ 2

math gurus please correct me if i am wrong
Trying hard!!!
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by samirpandeyit62 » Sat Oct 20, 2007 11:53 pm
Two persons agree to meet at between 2 PM to 4 PM, but each of them will wait 30 minutes for the late comer. What is the probability that they will meet?

the time between 2pm to 4pm can be divided into 120 slots (minutes)

let the two persons be A & B

now to meet A & B must arrive at the same time (same min) or within 30 min of the arrival of the first

so we can say that the reqd probability is

P of A coming at a time slot X P of B coming within 30 mins

=1/120 X 1 (for A to meet be B, If A has arrived B has to come)

=1/120

what is the OA
Regards
Samir
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by jangojess » Sun Oct 21, 2007 1:12 am
seems samir has a point....but i still am clueless :shock:
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by agni_mba » Sun Oct 21, 2007 1:40 pm
well the OA is 7/16.

I was approaching this problem pretty much in the same way as Samir did (though I do think that is not appropriate as B can arrive within one min. of A's arrival). Anyways, considering two hours as 120 minutes

Total possible ways: 120*120
120 mins can be divided in 3 logical parts
2:00->2:29: if A arrives within this period, B can arrive in 31+32+...60 ways (considering either side of 2: xx)
2:30->3:30: if A arrives within this period, B can arrive in 61+61+61... = 61*61
3:31->4:00: if A arrives within this period, B can arrive in 60+59...31 ways
so prob. = (30*91 + 61*61)/120*120

This answer is pretty close to 7/16. However not 7/16 exactly. Looks like the difference is because of consideration of minimum interval of 1 min....and hence am looking for a better/accurate approach.
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by wongee » Mon Oct 22, 2007 6:56 pm
I havent seen too many probability qtns in these types of probs, are they common? Hope not.
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by samirpandeyit62 » Mon Oct 22, 2007 9:25 pm
Hi Wongee,
IMO these kind of problems appear on the CAT(an Enterance exam for India's premier Mgmt Institutes, the IIM's), the Quant level of this test is much tougher that the toughest problems on the GMAT. So IMO we should not be expecting such a problem on the GMAT, coz these problems cannot be tackled by improvisation (that too in 2-3 mins),they simply need a higher level of preparation, also I've read on several posts here & on other sites that Probabilty questions rarely appear on the GMAT (even 51Q guys have claimed this), so if they do then also they shoudn't be of this level, I think some people should agree with me here, nevertheless If there is a good possibilty that such problems can come on the GMAT, then we need to enhance our level of preparation to tackle them.

BTW agni_mba you have provided a good & rational solution for the problem.
Regards
Samir
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by ldoolitt » Tue Oct 23, 2007 8:08 am
Techinically I believe this problem would require integration of sorts. You are providing a sum using time intervals as 1 minute, which is why you are slightly off. I believe if you let the time intervals pass to 0 you would end up with the correct answer.

At any rate, since the GMAT does not test integral calculus or calculus of any sort, I would venture a guess that this will not be on the test.
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by wongee » Fri Oct 26, 2007 4:37 pm
Thanks guys! I can heave a sigh of relief coz I dont think 2 mins is sufficient to reach the soln. But again, as samir said, you never know. Yes, I do know about CAT - I believe the math there is known to be tougher!
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