You Are Given a Decision Situation with Three Possible States $\mid$

You are given a decision situation with three possible states of nature S₁, S₂, and S₃. The prior probabilities of the three states are 0.20, 0.45, and 0.35. With sample information I, you are provided with the following information.
P(I₁ $\mid$ S₁) = 0.85
P(I₁ $\mid$ ₂) = 0.70
P(I₁ $\mid$ S₃) = 0.40
a.Compute P(I).
b.Compute the revised probabilities of P(S₁ $\mid$ I), P(S₂ $\mid$ I), and P(S₃ $\mid$ I).