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
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)