It’s a new month, which means it must be time for a new episode of Wrong, But Useful!

This time around, we talked about queuing at EuroDisney, how to play Battleships, why Peppa Pig’s dad has a quadratic equation in his office, 110%, elliptic curves and Dave’s brilliant new game.

The 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?

What I don’t understand:

Why matrix multiplication works the way it does.