Mixed Strategy subgame perfect equilibrium

Question

enter image description here

If player I can commit to a mixed strategy (1-p,p) for strategies (A,B) and player II knows the probability (1-p,p) applied to both strategies, what is the value of p in a subgame perfect equilibrium?

Answer 1

Hint: the probability must make player 2 indifferent between playing either strategies $p$ and $q$, or strategies $p$ and $r$.