BAYES' THEOREM

Question 12 (3 points)

Given the following prior probabilities:

P(s₁) = 0.5, P(s₂) = 0.1, and P(s₃) = 0.4

And sample information probabilities:

P(A|s₁) = 0.05, P(A|s₂) = 0.30, and P(A|s₃) = 0.20

P(B|s₁) = 0.65, P(B|s₂) = 0.20, and P(B|s₃) = 0.45

P(C|s₁) = 0.30, P(C|s₂) = 0.50, and P(C|s₃) = 0.35

Use Bayes' Theorem to compute the following revised probabilities:

ROUGH WORK MUST BE SHOWN IN ORDER TO RECEIVE CREDIT

1) P(s₃|A) FINAL ANSWERS 4 DECIMAL PLACES (2 marks)

2) P(A) FINAL ANSWERS 4 DECIMAL PLACES (1 mark)