The first and the major step in solving such problem is to make its formulation COMPACT and CLEAR, throwing out all the wording husk.


So, my re-formulation is THIS :


    Of 100% of all graduates

        there are 23% online graduates (mark them "O") and the rest 100%-23% = 77% "in person" graduates (mark them "P").

        39% of "O" say "Yes";    the rest of "O", i.e. 61% of "O" say "No".

        27% of "P" say "Yes";    the rest of "P", i.e. 73% of "P" say "No".

        Somebody says "No". What is the probability that this "somebody" is from "O" ?


The solution procedure is simple.

We should calculate the amount of those from "O" who said "No", and then relate it to the total amount of those who said "No".


The amount of those from "O" who said "No" is equal to   0.23*0.61.

The total amount of those    who said "No" is equal to   0.23*0.61 + 0.77*0.73.


Now the answer is this ratio  P = .


Do not make partial calculations  -  do not waste your time.


Copy the formula into Excel and get the ANSWER in one click !   It is  0.1997,  or  19.97%.