If P (A) = 0.8, P (B) = 0.5 and P (B|A) = 0.4, find

(i) P(A B) (ii) P(A|B) (iii) P(A B)


Given: P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4

(i) We know that


By definition of conditional probability,



P(A B) = P(B|A) P(A)


P(A B) = 0.4 × 0.8


P(A B) = 0.32


(ii) We know that


By definition of conditional probability,




P(A|B) = 0.64


(iii) Now, P(A B) = P(A) + P(B) – P(A B)


P(A B) = 0.8 + 0.5 – 0.32 = 1.3 – 0.32


P(A B) = 0.98


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