CUET · MATHS · PYQ PAPER 2023
Match List - I with List - II. Given \(P(A)=\frac{1}{3}\) and \(P(B)=\frac{1}{5}\) where \(A\) and \(B\) are independent.
| LIST I | LIST II |
| A. \(P(A \cap B)\) | I. \(\frac{7}{15}\) |
| B. \(P \left( A ^{\prime} \cap B ^{\prime}\right)\) | II. \(\frac{2}{5}\) |
| C. \(P\) (at least one of the two events takes place) | III. \(\frac{1}{15}\) |
| D. \(P\) (only one event takes place) | IV. \(\frac{8}{15}\) |
- A (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
- B (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- C (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
- D (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
Answer & Solution
Correct Answer
(B) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Step-by-step Solution
Detailed explanation
A. \(P(A \cap B) = P(A)P(B) = \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}\) B. \(P(A' \cap B') = P(A')P(B') = (1 - P(A))(1 - P(B)) = (1 - \frac{1}{3})(1 - \frac{1}{5}) = \frac{2}{3} \times \frac{4}{5} = \frac{8}{15}\) C.…
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