Given that P (A)=0.6, P (B)=0.5, P (A|B) = 0.2, P (C|A)= 0.3 and P (C|B)=0.4. (1) If they are depe

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Given that P (A)=0.6, P (B)=0.5, P (A|B) = 0.2, P (C|A)= 0.3 and P (C|B)=0.4.

(1) If they are dependent each other, what is P (B | A) = ?

(2) If the event C is conditionally dependent upon evens A and B, What's the probability: P (A|C) = ?

(1) Bayes Rule: P(B|A) = P(B) * P(A|B)
P(B|A) = 0.5 * 0.2 = 0.1

(2) Bayes Rule: P(A|C) = P(A) * P(C|A)
P(A|C)= 0.6 * 0.3 = 0.18