Suppose that you are given a decision situation with three possible state of nature: S1, S2, and S3. The prior probabilities are P (S1) = 0.2, P (S2) = 0.5, and P (S3) = 0.3. With sample information I, P (I|S1) = 0.1, P(I|S2) = 0.05, and P (I|S3) = 0.2.
Compute the revised or posterior probabilities:
- Compute P (S1|I)
- Compute P (S2|I)
- Compute P (S3|I)