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# MGMAT probability - symmetry approach.

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MGMAT probability - symmetry approach. [#permalink]  11 Jul 2011, 02:18
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A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

Though this is a solved ex in MGMAT quant book but i couldnt really get the approach of symmetry.. Please solve and explain the approach.

The solution given is:

None of the 14 patients is "special" in any way, so each of them must have the same
chance of receiving Progaine or Ropecia. Since Progaine is only administered to one patient,
each patient (including Donald) must have probability 1114 of receiving it. The same logic
also holds for Ropecia. Since Donald cannot receive both of the medicines, the desired
probability is the probability of receiving Progaine, plus the probability of receiving Ropecia:
1/14 + 1/14 = 1/7.
The placebo is irrelevant, as is the order that the researcher artificially chose for the selection
process. You can solve this problem by using a sequence of two choices

I contend that the prob should be 1/14 * 1/13 instead. (which i know is a wrong thought )

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Re: MGMAT probability - symmetry approach. [#permalink]  11 Jul 2011, 04:57
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RohitKalla wrote:
A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

Though this is a solved ex in MGMAT quant book but i couldnt really get the approach of symmetry.. Please solve and explain the approach.

The solution given is:

None of the 14 patients is "special" in any way, so each of them must have the same
chance of receiving Progaine or Ropecia. Since Progaine is only administered to one patient,
each patient (including Donald) must have probability 1114 of receiving it. The same logic
also holds for Ropecia. Since Donald cannot receive both of the medicines, the desired
probability is the probability of receiving Progaine, plus the probability of receiving Ropecia:
1/14 + 1/14 = 1/7.
The placebo is irrelevant, as is the order that the researcher artificially chose for the selection
process. You can solve this problem by using a sequence of two choices

I contend that the prob should be 1/14 * 1/13 instead. (which i know is a wrong thought )

You can use the general case formula to sort it out:
P (Receiving P or R) = P(Receiving P) + P(Receiving R) - P(Receiving Both)
P(Receiving P) = 1/14
P(Receiving R) = 13/14 * 1/13 = 1/14(If he has to receive R, he should not receive P. Probability of not receiving P is 13/14. Then probability of receiving R is 1/13. Both these things should occur if he wants to receive R so the two are multiplied)
P(Receiving Both) = 0 (Because no one can receive both)
P (Receiving P or R) = 1/14 + 1/14 - 0 = 1/7
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Re: MGMAT probability - symmetry approach. [#permalink]  11 Jul 2011, 05:46
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RohitKalla wrote:
A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

Or you can just imagine lining the 14 people up at random, and giving the first person in line Progaine and the second person in line Ropecia. The probability Donald is one of the first 2 people in line is 2/14 = 1/7.
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Re: MGMAT probability - symmetry approach. [#permalink]  11 Jul 2011, 03:53
Odds of Donald receiving Progane are 1/14.

Odds of him receiving Ropecia are (13/14)*(1/13)=1/14 (since he has to not receive Progane to receive Ropecia)

Therefore the odds of receiving either are (1/14+1/14=) 1/7.
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Re: MGMAT probability - symmetry approach. [#permalink]  12 Jul 2011, 10:12
IanStewart wrote:
RohitKalla wrote:
A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

Or you can just imagine lining the 14 people up at random, and giving the first person in line Progaine and the second person in line Ropecia. The probability Donald is one of the first 2 people in line is 2/14 = 1/7.

Great ! Thanks all for the explanations.
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Re: MGMAT probability - symmetry approach. [#permalink]  14 Jul 2011, 22:26
odds of Donald getting prog = (1/14 )* (13/13) *(12/12 ) = 1/14

odds of Donald getting rop = (13/14)*(1/13)*(12/12) = 1/14

hence odds of Donald getting either prog or rop = (1/14) + (1/14) = 1/7
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Re: MGMAT probability - symmetry approach. [#permalink]  14 Jul 2011, 22:30
or you can even try it the following way.

odds of Donald getting prog or rop = 1 - odds of Donald getting None of these

= 1 - (13/14)*(12/13)(12/12) = 1/7
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Re: MGMAT probability - symmetry approach. [#permalink]  17 Jul 2011, 14:11
Cool. Thanks Ian for simple and elegant solution approach!
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Re: MGMAT probability - symmetry approach.   [#permalink] 17 Jul 2011, 14:11
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