The prior probabilities for events are ?1, ?2,and?3?(?1)=0.20, ?(?2)=0.50,?(?3)=0.30. (Note the events are mutually exclusive and...

The prior probabilities for events are ?₁, ?₂,and?3?(?₁)=0.20, ?(?₂)=0.50,?(?₃)=0.30. (Note the events are mutually exclusive and collectively exhaustive). The conditional probabilities of event B given are ?₁, ?₂,and?₃?(?|?₁)=0.50, ?(?|?₂)=0.40,?(?|?₃)=0.30

1. Compute and .?(?⋂?₁), ?(?⋂?₂) and ?(?⋂?₃)

2. Compute ?(?)

3. Apply Bayes’ theorem to compute the posterior probability, and .?(?₁|?), ?(?₂|?) and ?(?₃|?)

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