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The Safe (Posted on 2003-08-11) Difficulty: 2 of 5
A group of crazy bank robbers try to crack a safe, even though they don't have a clue what the code is. The code has 5 numbers in, and the numbers on the dial range from 1 to 60. If they crack the safe, they get 100 billion.(That's a British billion - a million million). If they get the code wrong, they get caught and fined 1 million.

Assuming the bank robbers don't enter the same code twice, if they keep trying and re-trying until they crack the safe, are they more likely to have lost or gained money? If so, how much would they probably gain/lose?

See The Solution Submitted by Lewis    
Rating: 2.7500 (4 votes)

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No Subject | Comment 7 of 10 |
Surely they only get one go at the safe within a reasonable time frame. I assume a 1 million fine would also include a hefty jail term. However this assumption doesn't effect my solution.

For each go at 60^5 combinations:
Probability = 1/60^5
= 0.0000001286% of getting 100 billion.
Therefore, their expected cash inflow is 1286.0023

However, they may get it wrong:
Probability = 99.9999998714% of losing 1 million.
Therefore, their expected cash outflow is 999999.9987

Giving their overall expected cash flow:
= 1286.0023 - 999999.9987
= -998713.9905

Therefore, they can expect to lose 998713.9905 each time they try to crack the safe.
  Posted by Dave Cheetham on 2003-08-17 13:12:19
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