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In: Statistics and Probability

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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