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Task is so difficult that only 5% of candidates solve it correctly. Moreover, even the interviewer mistakes the wrong solution for the right one 2% of the time (he always reconginse the right solutions). The interviewer tells you that you did well. What is the probability that you gave the right answer?

How to use phrase "he always recognise the right solutions". Does it mean that it is 100% positive feedback probability if answer is correct?

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    $\begingroup$ Is this a question from a course or textbook? If so, please add the self-study tag & read its wiki. $\endgroup$ Commented Apr 23, 2021 at 11:37
  • $\begingroup$ $P(\text{correct}\vert\text{positive feedback}$ is your value of interest. What methods have you learned for handling a conditional probability like this? $\endgroup$
    – Dave
    Commented Apr 23, 2021 at 11:40
  • $\begingroup$ @Dave well, it is tough for me to understand such probs. I can see it as 98% pos feedback x 5% of correct answer = 4.9% $\endgroup$
    – statlad
    Commented Apr 23, 2021 at 11:59
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    $\begingroup$ What do you mean by the interviewer "he always learns the right solutions"?? $\endgroup$
    – Fiodor1234
    Commented Apr 23, 2021 at 12:19
  • $\begingroup$ @Fiodor1234 that means interviewer recongnizes correct solutions always. $\endgroup$
    – statlad
    Commented Apr 23, 2021 at 12:22

1 Answer 1

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There are three common approaches and it is hard to tell, which was taught.

As @Dave commented: There is some $Rule$ named after a famous person for computation of conditional probabilities.

Then you could draw a tree as in

                             100 % of cases
                                /   \
                               /     \
                    I was right      I was wrong
                         /  \           /  \
                        /    \           ...
            Interviewer       - is wrong
            is right

And finally a 4x4 contingency table might be helpfull.

                             Interviewer 
                        right   |    wrong
                  right         |            5 %
            me          --------+----------
                  wrong         |           95 %  
                        --------+----------  
                          
                          2 %       98 %
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  • $\begingroup$ but the condition is that interviewer can recognize correct solutions always, and only 2% he is mistaken with wrong solution being correct. $\endgroup$
    – statlad
    Commented Apr 23, 2021 at 12:25

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