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Fair coin puzzle

FairCoinPuzzleThis board was sent to me via Twitter by Will Davies (aka @notonlyahatrack) who had listened to the podcast Wrong, But Useful (by Colin Beveridge (@icecolbeveridge) and Dave Gale (@reflectivemaths) ) and attempted the following puzzle:

I have three indistinguishable coins: one always comes up heads, one always comes up tails and the third is a fair coin. I pick one of the coins at random and toss it twice and get the same result both times. What is the probability I picked the fair coin?

You should have a go at the puzzle yourself before looking too closely at the solution in the photo!

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3 responses

  1. Reblogged this on Things from under my hats.

    May 19, 2013 at 12:46 pm

  2. Richard

    That answer is incorrect! The question says “I get the same result both times”, not “I get heads both times”…

    September 3, 2015 at 7:20 pm

    • haggisthesheep

      I agree. The tails case is symmetric, so its probability is also 1/5. So in total I think the answer should be 2/5. Agreed?

      October 2, 2015 at 6:51 pm

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