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?
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.
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