COMEDK · Maths · 36. Probability
If \(A, B\) and \(C\) are mutually exclusive and exhaustive events of a random experiment such that \(P(B)=\dfrac{3}{2} P(A)\) and \(P(C)=\dfrac{1}{2} P(B)\), then \(P(A \cup C)\) equals to
- A \(\dfrac{6}{13}\)
- B \(\dfrac{3}{13}\)
- C \(\dfrac{10}{13}\)
- D \(\dfrac{7}{13}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{7}{13}\)
Step-by-step Solution
Detailed explanation
Since \(A, B,\) and \(C\) are mutually exclusive and exhaustive events, the sum of their probabilities is \(P(A) + P(B) + P(C) = 1\). Given \(P(B) = \dfrac{3}{2} P(A)\) and \(P(C) = \dfrac{1}{2} P(B)\), we can express \(P(C)\) in terms of \(P(A)\):…
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