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Backward differential equations

SiskaOct2014This board was created in the common room of the School of Mathematics at the University of Edinburgh by David Siska and Arnaud Lionnet. Arnaud is visiting David in Edinburgh, and they are working on backward stochastic differential equations and stochastic partial differential equations, which are on the interface between probability and analysis.

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 GaleĀ (@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!