Compute posterior and predictive coin probabilities

You have two coins: F is fair; B is biased with P(H)=0.7. You pick one coin uniformly at random and flip it three times. The first two flips are Heads (the third flip outcome is not yet observed). a) Compute P(picked B | first two flips are Heads). b) Compute P(next flip is Heads | first two flips are Heads). c) Continuing with the same coin, let T be the total number of flips until the first Tail occurs (including it). Compute E[T | first two flips are Heads], showing your derivation.