Question

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. \(P(A|B)=\dfrac{L+M-1}{M}\)

Answer 1

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 \(\rm P(A|B)=\dfrac{P(A∩ B)}{P(B)}\)

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