# Let two events A and B be such that P(A) = L and P(B) = M. Which one of the following is correct?

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Let two events A and B be such that P(A) = L and P(B) = M. Which one of the following is correct?
1. $P(A|B)<\dfrac{L+M-1}{M}$
2. $P(A|B)>\dfrac{L+M-1}{M}$
3. $P(A|B)\ge\dfrac{L+M-1}{M}$
4. $P(A|B)=\dfrac{L+M-1}{M}$

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Correct Answer - Option 3 : $P(A|B)\ge\dfrac{L+M-1}{M}$

Concept:

$\rm P(A|B)=\dfrac{P(A∩ B)}{P(B)}$

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Calculation:

Given P(A) = L and P(B) = M

Here P(A ∪ B) ≤ 1 (∵ Max value of probability is 1)

P(A) + P(B) - P(A ∩ B) ≤ 1

L + M - P(A ∩ B) ≤ 1

P(A ∩ B) ≥ L + M - 1

Now $\rm P(A|B)=\dfrac{P(A∩ B)}{P(B)}$

$\rm P(A|B)\geq\dfrac{L+M-1}{M}$