Fair coin puzzle

^^ Not the most complicated maths in the world, but it forsure solves the problem 😀

What's on my blackboard?

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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