## Fair coin puzzle

This 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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notonlyahatrackReblogged this on Things from under my hats.

May 19, 2013 at 12:46 pm

RichardThat 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

haggisthesheepI 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