metallicafan 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?
MGMAT's approach:"Since Progaine is only administered to one patient, each patient (including Donald) must have probability 1/14 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:
\(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\)
My approach:Probability of receiving Progaine:\(\frac{1}{14} * \frac{13}{13} = \frac{1}{14}\)
Probability of receiving Ropecia, which is:(Probabilty of NOT receiving Progaine) * (Probability of receiving Ropecia among the rest):
13/14 * 1/13 = 1/14
Therefore, the answer to question is: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\)
Is my approach correct?, Why doesn't
MGMAT consider the order in the administration of the drugs?
When the researcher provides Ropecia, he or she has to choose among 13 people, NOT 14. It seems they are using the P(A) + P(B) - P(A and B) formula. Please your comments.
I am going over this question right now and I saw the solutions and I really appreciate the input guys. Bunuel my question is similar and what really throws me off is the phrase "
The same logic also holds for Ropecia" - 1) Do you think
MGMAT just used a shortcut there to say that P(Ropecia) = 13/14 * 1/13 = 1/14 or how else do you get 1/14 for P(Ropecia)? The way I translate "
The same logic also holds for Ropecia" is certainly not P(Ropecia) = 1/14 for the reason described above...please let me know if the explanation
MGMAT provides sounds clear to you and perhaps what you would take out from such explanation.
2) As for your solution, if we change to the question to "
what is the P(Progaine, or Ropecia, or Placebo)?" the solution would not be 3/14 or would it?
P.S. Just another thought, I agree that your method is much shorter (and intuitive as well) but for those who do not have a solid grasp of seemingly more convoluted prob/comb problems such as one above (and as such, they may be viewed as those who lack "common sense"
) it is important to see all of the steps...so in this regard it is good that metallicafan clarified one way we get P(Ropecia) and fits nicely with overall thinking about probability.