You Are Given the Following Payoff Table $\mid$ S₁) = 0 $\mid$

You are given the following payoff table. Assume the following probability information is given.
P(S₁) = 0.45
P(I₁ $\mid$ S₁) = 0.7
P(I₂ $\mid$ S₁) = 0.3
P(S₂) = 0.55
P(I₁ $\mid$ S₂) = 0.6
P(I₂ $\mid$ S₂) = 0.4
a.Find the values of P(I₁) and P(I₂).
b.Determine the values of P(S₁ $\mid$ I₁), P(S₂ $\mid$ I₁), P(S₁ $\mid$ I₂), and P(S₂ $\mid$ I₂).
c.Use the decision tree approach and determine the optimal strategy. What is the expected value of your solution?