Apologies for not posting the answer last weekend, I was traveling again 🙂
I guess conditional probability puzzles are not the most popular, I got correct answers only from Suman Saraf and Pratik Poddar, even though I thought that the problem was an easy one.
This was a classical conditional probability puzzle. The answer is ~41%
Here is the way to do it:
Probability of losing the key in the first meeting is 20%
Probability of losing the key in the second meeting is 80% x 20% = 16%
Probability of losing the key in the third meeting is 80% x 80% x 20% = 12.8%
Given that we know that the key was lost, it must be in one of the three meetings, and we need to figure out the relative probability of losing in the first meeting vis-a-vis the two others, which can be calculated as:
20%/ (20%+16%+12.8%) = ~41%
Hope you all enjoyed the puzzle!