## Wednesday, January 09, 2008

### Locked Drawers and Lost Files

A man working in a cube has 10 drawers in which to store his files. Two of the drawers can be locked. Each time he stores a file, he picks one of the drawers at random and places it inside.

Yesterday he locked the two drawers that could be locked, but when he came in this morning, he realized he had forgotten his keys at home. He realizes he needs one of his files and begins to look for it. His search is simple, picking each drawer in order, he rifles through each one until he finds the file he needs. He does not go back to any drawer he has already checked.

1) He checks the first drawer, but doesn't find the file. What are the chances he finds the file in the remaining 7 drawers? (Remember, he can't check the last two!)

2) He checks the first four drawers and has not found it. What are the chances he will find the file in the remaining 4 drawers he can open?

3) He has looked in the first seven drawers. What are the chances he can find the document in the final drawer?

#### 1 comment:

1. The answers to the three questions are 7/9, 2/3 and 1/3, respectively.

The chances actually decrease for every drawer you fail to find it in. The probability is (8-n) / (10-n).

This is a decreasing function of n for n < 10.

With K drawers to go, of which two are unavailable, the probability of a successful outcome is (K - 2)/K. With K = 10 - n, this reduces to (8 - n)/(10 - n).

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