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. 
a.Compute P(I).
b.Compute the revised probabilities of P(S1|I), P(S2|I), and P(S3|I).
Definitions:
Archaea
A category of unicellular microorganisms that are genetically different from bacteria and eukaryotes, typically thriving in harsh conditions.
Prokaryotes
Single-celled organisms that lack a membrane-bound nucleus and other organelles.
Eukaryotes
Beings that have cells which include a nucleus and different organelles, all surrounded by membranes.
Lac Operon
A group of genes in bacteria controlled by a single promoter, involved in lactose metabolism and regulation of gene expression.
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