CUET · MATHS · PYQ PAPER 2025
Let A, B, C be three events. If the probability of occurring exactly one out of A and B is \(\frac{3}{5}\), exactly one out of B and C is \(\frac{1}{5}\), exactly one out of C and A is \(\frac{3}{5}\), and that of occurring of three events is \(\frac{4}{25}\), then the probability of occurring at least one of them is
- A \(\frac{6}{25}\)
- B \(\frac{27}{50}\)
- C \(\frac{43}{50}\)
- D \(\frac{23}{25}\)
Answer & Solution
Correct Answer
(C) \(\frac{43}{50}\)
Step-by-step Solution
Detailed explanation
\( P(A \Delta B) = P(A)+P(B)-2P(A \cap B) = \frac{3}{5} \) \( P(B \Delta C) = P(B)+P(C)-2P(B \cap C) = \frac{1}{5} \) \( P(C \Delta A) = P(C)+P(A)-2P(C \cap A) = \frac{3}{5} \) \( 2(P(A)+P(B)+P(C)) - 2(P(A \cap B)+P(B \cap C)+P(C \cap A)) = \frac{3}{5}+\frac{1}{5}+\frac{3}{5} \)…
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