I got this question during an interview with Amazon:


50% of all people who receive a first interview receive a second interview
95% of your friends that got a second interview felt they had a good first interview
75% of your friends that DID NOT get a second interview felt they had a good first interview


If you feel that you had a good first interview, what is the probability you will receive a second interview?

Can someone please explain how to solve this? I'm having trouble breaking down the word problem into math (the interview is long over now). I understand there may not be an actual numerical solution, but an explanation of how you would walk through this problem would help.

edit: Well I did get a second interview. If anyone is curious I had gone with an explanation that was a combination of a bunch of the responses below: not enough info, friends not representative sample, etc and just talked through some probabilities. The question left me puzzled at the end though, thanks for all of the responses.

Say 200 people took the interview, so that 100 received a 2nd interview and 100 did not. Out of the first lot, 95 felt they had a great first interview. Out of the 2nd lot, 75 felt they had a great first interview. So in total 95 + 75 people felt they had a great first interview. Of those 95 + 75 = 170 people, only 95 actually got a 2nd interview. Thus the probability is:
$$\frac{95}{(95 + 75)}=\frac{95}{170}=\frac{19}{34}$$

Note that, as many commenters graciously point out, this computation is only justifiable if you assume that your friends form an unbiased and well distributed sampling set, which may be a strong assumption.
