You want to choose between actions A1 and A2 in the following decision tree, but you are uncertain about the value of the probability p, so you need to perform sensitivity analysis of p as well.

Your utility function for money (the payoff received) is u(M) 

(a) For p 0.25, determine which action is optimal in the sense that it maximizes the expected utility of the payoff.

(b) Determine the range of values of the probability p (0 p 0.5) for which this same action remains optimal.