Schmide
Diamond Member
- Mar 7, 2002
- 5,588
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After this post, I'll look it up. I just wanted to think about it before I spoiled.
So you come up with a strategy for elimination.
So you come up with a strategy for elimination.
Each inmate chooses a separate locker and correct choices are eliminated.
The first round the chance of any single success is (1 in 100) * 50. or 50% chance of elimination of a locker. So on average for the first 2 choices 1 locker gets eliminated and one inmate is removed. The 3rd chance of success is now 1 in 98 * 49 which has a 50% chance of success equal to the 4th chance. On the 5th round you have a (1 in 96) * 48 which has a 50% chance of elimination success. You get the pattern.
This becomes a 100c50 problem. I.e 100/1 * 99/2 * 98/3...
Which equals 1 in 100,891,344,545,564,193,334,812,497,256 chance
The first round the chance of any single success is (1 in 100) * 50. or 50% chance of elimination of a locker. So on average for the first 2 choices 1 locker gets eliminated and one inmate is removed. The 3rd chance of success is now 1 in 98 * 49 which has a 50% chance of success equal to the 4th chance. On the 5th round you have a (1 in 96) * 48 which has a 50% chance of elimination success. You get the pattern.
This becomes a 100c50 problem. I.e 100/1 * 99/2 * 98/3...
Which equals 1 in 100,891,344,545,564,193,334,812,497,256 chance
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