The following extensive form game is given:
Find a Subgame Perfect Nash equilibrium of the game featuring one player using a mixed strategy.
I know that in order to find a SPNE (Subgame Perfect Nash Equilibrium), we can use backward induction procedure and I am familiar with this procedure. In fact, I can solve this game for SPNE in pure strategies, but I don't know know how to solve it using a mixed strategy. I also know how to find a mixed strategy Nash equilibrium in static games, but I don't know how to do it in dynamic games, i.e. combine it with backward induction. I tried to represent some subgames in a payoff matrix and to solve for indifference condition for both players like in static games, but I obtained negative probability values, which is, of course, wrong.
Any help is appreciated.
Thanks in advance.