CUET · MATHS · PYQ PAPER 2023
If \(2 P(A)=P(B)=\frac{5}{13}\) and \(P(A \mid B)=\frac{2}{5}\), then the value of \(P(A \cup B)\) is :
- A \(\frac{11}{13}\)
- B \(\frac{13}{14}\)
- C \(\frac{11}{26}\)
- D \(\frac{13}{26}\)
Answer & Solution
Correct Answer
(C) \(\frac{11}{26}\)
Step-by-step Solution
Detailed explanation
\(P(A) = \frac{1}{2} P(B) = \frac{1}{2} \cdot \frac{5}{13} = \frac{5}{26}\) \(P(A \cap B) = P(A \mid B) \cdot P(B) = \frac{2}{5} \cdot \frac{5}{13} = \frac{2}{13}\) \(P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{5}{26} + \frac{5}{13} - \frac{2}{13}\)…
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