CUET · MATHS · PYQ PAPER 2023
If \(P(A)=\frac{6}{11}, P(B)=\frac{5}{11}\) and \(P(A \cup B)=\frac{7}{11}\), then
A. \(P(A \cap B)=\frac{4}{11}\)
B. \(P(A \mid B)=\frac{ 4 }{ 5 }\)
C. \(P(B \mid A)=\frac{2}{5}\)
D. \(A\) and \(B\) are independent events
E. \(P(\) neither \(A\) nor \(B)=\frac{4}{11}\)
Choose the correct answer from the options given below:
- A A and E only
- B A, B and E only
- C B and D only
- D A, C and E only
Answer & Solution
Correct Answer
(B) A, B and E only
Step-by-step Solution
Detailed explanation
\(P(A \cap B) = P(A) + P(B) - P(A \cup B)\) \(P(A \cap B) = \frac{6}{11} + \frac{5}{11} - \frac{7}{11} = \frac{4}{11}\) A. \(P(A \cap B) = \frac{4}{11}\) (Correct) \(P(A \mid B) = \frac{P(A \cap B)}{P(B)}\) \(P(A \mid B) = \frac{4/11}{5/11} = \frac{4}{5}\) B.…
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