A medical researcher must choose one of 14 patients to receive an expe

Bunuel, I don't understand the approach of the MGMAT guys.
In the case of Ropecia, why the probability is 1/14? I think it should be 1/13 because when we give Ropecia there are only 13 patients, not 14. Remember that Ropecia is given after Progaine.

Thanks!

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.

This question has much simpler solution than MGMAT offered:

Donald to receiver either Prograine or Ropecia must be among first two chosen patients and as there are 14 patients then the probability of this is simply 2/14=1/7.

Thank you Bunuel!
But what do you think about my approach?, am I going in the right path?
Thanks!

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.

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?

What should be the methodology to tackle these questions ?

Bunuel, I don't understand the approach of the MGMAT guys.
In the case of Ropecia, why the probability is 1/14? I think it should be 1/13 because when we give Ropecia there are only 13 patients, not 14. Remember that Ropecia is given after Progaine.

Thanks!

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