Q. 625.0( 1 Vote )

# If A and B are two events and A ≠ θ, B ≠ θ, then

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

B.

C. P(A | B).P(B | A)=1

D. P(A | B) = P(A) | P(B)

Correct

Answer :

Given: A ≠ φ, B ≠φ

CASE 1: If we take option (A) i.e. P(A|B) = P(A).P(B)

LHS =

CASE 2: If we take option (B) i.e.

this is true, we all know that this is conditional probability.

CASE 3: If we take option C .i.e. P(A|B)×P(B|A) = 1

LHS = P(A|B) × P(B|A)

≠ RHS

Hence, **the correct option is B**

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