Probability Puzzle: Combining Information from Multiple Unreliable Sources in a Coin-Flipping Game
By
evakhoury
The bagel they save for the regulars. Don't skim, savour.
Summary
This article explores a probability puzzle involving a coin-flipping game with two unreliable informants. Alice sees a coin flip and reports it to you, but lies 20% of the time. Your optimal strategy of trusting Alice gives you 80% accuracy. The article then introduces Bob, who also independently reports the coin flip with the same 20% lying probability. The core question is how much your accuracy improves when you have both Alice and Bob's reports to work with, exploring the surprising mathematical probabilities behind combining information from multiple unreliable sources.
Key quotes
· 4 pulledYour best strategy is to trust whatever Alice says. You're right 80% of the time.
Now Bob joins in. He makes up his mind independent of Alice, and he also lies 20% of the time.
You were right 80% of the time by trusting Alice. How much better can you do with Bob's help?
A look at the surprising probabilities behind a simple coin flipping game
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