Can you figure out the liar's PIN code?
Probability
Level
1
- Your friend is a liar. You know he lies 99% of the time.
- He tells you his PIN is "1337".
- A PIN can be any number from 0000 to 9999.
He gives you one try to unlock his phone. Should you enter 1337 or guess a random PIN other than 1337?
It's the same probability either way
Enter another random PIN
Enter 1337
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1 solution
If you guess a random PIN (which is not 1337), the probability of you being correct is 0.99 * 9 9 9 9 1 . That is the probability the friend is lying (99%) times the probability of guessing a correct PIN out of the 9999 possible PINs left. That works out to be roughly 0.0099%.
If you guess "1337", the probability of you being correct is 0.01 (1% that the friend is telling the truth). 1% is significantly better than 0.0099%.