Suppose you have 2 identical-looking coins: one that is fair and one that comes up heads 75% of the time.

You randomly chose one of them, flip it 3 times and it comes up as H-H-T.

What is the chance that the coin you picked is the fair one?

Source: Project Euler

Simple Bayesian calculation

The fair coin comes up HHT with probability (1/2)*(1/2)*(1/2) = 1/8 = 8/64

The other coin comes up HHT with probability (3/4)*(3/4)*1/4 = 9/64

In my head, then, the probability of the fair coin has just become **8/17. Final answer**.

proper calculation is

(1/2)*(8/64) / ((1/2)*(8/64) + (1/2)*(9/64)),

but I just shortcutted it as 8/(8+9)