View source for Priyanka Savkar 6.3 ECE302Fall2008sanghavi - Rhea

Probability of getting heads given a particular coin q is:
P[H|Q=q] = q
PDF of Q = 2q

Therefore P[H1|Q=q] = q
P[H1|H2] = P[H2 intersection H1]/P[H1]

P[H1] is the integration from 0 to 1 of P[H1|Q=q] x PDF of Q, which turns out to be 2/3.

P[H2 intersection H1]  is the integration from 0 to 1 of (q^2) x PDF of Q, which equals 1/2.

Therefore, plugging the above answers into the conditional probability formula will give the probability of H2|H1.