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!