## Puzzle #161: Lost Car Key Puzzle

This is a very nice probability puzzle, variations of which we have done in the past. This one is contributed by Suman Saraf – Thanks Suman!

I drive to work, and put my car keys in my pocket. Whenever I sit down in a meeting there is a 20% chance that my car keys might fall out of my pocket (unnoticed). At lunchtime, I reach for my keys and find out they are missing. If I’ve had three sit-down meetings that morning, what is the chance that the car keys fell out in the first meeting location?

(You can assume the only place the keys could have fallen out is in one of those three locations)

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy driving!

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### 1 Response to Puzzle #161: Lost Car Key Puzzle

1. 0.2/(1-(0.8)^3)=0.2/0.488=0.409