Monday, July 21, 2008

A simple puzzle

As you're walking along the street in front of Honest Jake's Biased Coin Factory, you find a quarter on the sidewalk. You suspect it is biased, so you flip it 41 times and observe that it comes up heads 29 times. A bystander notices your interest in probability and offers $10 even money that your next two flips are not both heads. Do you take the bet?

Clarifications and assumptions:
  • Assume the coin is from Honest Jake's factory.
  • Honest Jake guarantees that every flip of their coins is independent.
  • Honest Jake makes coins with any bias and has no preference for any particular bias. His motto is ‘My coins are biased, I'm not.’
  • The bystander pays you $10 if the next two flips are heads, otherwise you pay the bystander $10.
  • You will be willing to take the bet if you expect to gain money and unwilling if you expect to lose money.
I found this problem on the web (I'll credit it later). The problem was intended to show the difference between Bayesian and traditional reasoning, but the original poster made a slight error and got the wrong result. This problem has a very subtle point to it. I'll post the answer in a few hours.

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