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Updated on: 29 Sep 2013, 10:16
Originally posted by RohitKalla on 11 Jul 2011, 02:18.
Last edited by Bunuel on 29 Sep 2013, 10:16, edited 2 times in total.
Last edited by Bunuel on 29 Sep 2013, 10:16, edited 2 times in total.
Renamed the topic and edited the question.
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N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
83% (01:30) correct
17%
(01:56)
wrong
based on 74
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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?
OA:
OPEN DISCUSSION OF THIS QUESTION IS HERE: a-medical-researcher-must-choose-one-of-14-patients-to-127396.html
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
)
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
)OA:
1/7
OPEN DISCUSSION OF THIS QUESTION IS HERE: a-medical-researcher-must-choose-one-of-14-patients-to-127396.html
11 Jul 2011, 04:57
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RohitKalla
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
General Discussion
11 Jul 2011, 03:53
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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.
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.
Thanks all for the explanations. 
