If A and B are events such that P (A|B) = P(B|A), then

(A) A ⊂ B but A ≠ B (B) A = B

(C) A ∩ B = Φ (D) P(A) = P(B)

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Solution

It is given that, P(A|B) = P(B|A)

⇒ P (A) = P (B)

Thus, the correct answer is D.

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Similar questions

Q. If A and B are events such that P (A|B) = P(B|A), then (A) A ⊂ B but A ≠ B (B) A = B (C) A ∩ B = Φ (D) P(A) = P(B)

In each of the questions choose the correct answer.
If A and B are events such that $P (\frac{A}{B}) = P \frac{B}{A},$ then
(a) $A \subset B b u t A \neq B$

(b) A = B

(d) P(A) = P(B)

IF A and B are any two events such that P(A) + P(B) - P (A and B ) = P(A), then
(a) $P (\frac{B}{A}) = 1$
(b) $P (\frac{A}{B}) = 1$
(c) $P (\frac{B}{A}) = 0$
(d) $P (\frac{A}{B}) = 0$

If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then

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

Q. If A and B are events such that P (A) = 0.6, P (B) = 0.3 and P (A ∩ B) = 0.2, find P (A/B) and P (B/A).

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If A and B are events such that P (A|B) = P(B|A), then (A) A ⊂ B but A ≠ B (B) A = B (C) A ∩ B = Φ (D) P(A) = P(B)

It is given that, P(A|B) = P(B|A) ⇒ P (A) = P (B) Thus, the correct answer is D.

If A and B are events such that P (A|B) = P(B|A), then

(A) A ⊂ B but A ≠ B (B) A = B

(C) A ∩ B = Φ (D) P(A) = P(B)

It is given that, P(A|B) = P(B|A)

⇒ P (A) = P (B)

Thus, the correct answer is D.