From Stack Exchange:

• 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?

The easiest way (at least for me) to go is to turn those percentages into some real numbers. For instance:
– 100 friends that got a second interview; 95 of them felt that they had a good first interview
– 100 friends that did NOT get a second interview; 75 of them felt that they had a good first interview.
Now, if you ignore the fact that it’s pretty difficult to have 200 friends (let alone the fact that they all applied for a job at Amazon 🙂 ), the numbers say that:
– 95 + 75 = 170 friends had a good feeling after the first interview
– but only 95 of them had a second interview
– so the probability of you having a second interview is 95 / 170 = 0.558.
In other words, if you felt good after the first interview, you have more than 50% chances that you get a second interview.

Image: HollywoodReporter.com

Now, if you come up with the answer 55.8% to your Amazon interviewer, I think you would get some points. But not all of them. Because in the logic below there are 2 hidden assumptions:

1. That your group of friends is NOT representative for all the people that applied
2. That you are representative for your group of friends

If the first assumption is false (so your group of friends is representative for all the people that applied), then the answer will always be 50%. It’s the first sentence of the problem: “50% of all people who receive a first interview receive a second interview”.
If the second assumption is false (so you are NOT representative for your group of friends) – then the 95% and 75% percents do not apply to you; so the answer is again in the first sentence of the problem.

More info on the Stack Exchange discussion.