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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

Let two events A and B be such that P(A)=L and P(B)=M . Which one...

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

Options

  1. AP(A∣B)<L+M−1MP(A \mid B) < \frac{L+M-1}{M}
  2. BP(A∣B)>L+M−1MP(A \mid B) > \frac{L+M-1}{M}
  3. CP(A∣B)≥L+M−1MP(A \mid B) \geq \frac{L+M-1}{M}
  4. DP(A∣B)=L+M−1MP(A \mid B)=\frac{L+M-1}{M}

Correct answer

C. P(A∣B)≥L+M−1MP(A \mid B) \geq \frac{L+M-1}{M}

Step-by-step solution

P(A∣B)=P(A∩B)P(B)P(A \mid B)=\frac{P(A \cap B)}{P(B)} Now, P(A∩B)=P(A)+P(B)−P(A∪B)∴min⁡.(P(A∩B)=L+M−1{HereP(A \cap B)=P(A)+P(B)-P(A \cup B)\therefore \min.(P(A \cap B)=L+M-1 \{Here P(A \cup B)=1max.value∴P(A∣B)≥L+M−1Mmax. value \therefore P(A \mid B) \geq \frac{L+M-1}{M}
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