AP EAMCET · Maths · Probability
Let \(A, B\) and \(C\) be three events associated with sample spaces \(S . A, B\) and \(C\) are pair wise independent and \(P(A)=P(B)=P(C)=P\). If all of them cannot occur simultaneously, then \(P(A \cup B \cup C)\) is equal to
- A \(1-(1-P)^3\)
- B \(3 P(1-P)\)
- C \(P^3\)
- D \(3 P\)
Answer & Solution
Correct Answer
(B) \(3 P(1-P)\)
Step-by-step Solution
Detailed explanation
A, B, C are pair-wise independent events. \[ \begin{aligned} \Rightarrow \quad & P(A \cap B)=P(A) \cdot P(B) \\ & P(B \cap C)=P(B) \cdot P(C) \\ & P(C \cap A)=P(C) \cdot P(A) \end{aligned} \] and \(P(A)=P(B)=P(C)=P\) and \(P(A \cap B \cap C)=0\) [ \(\because\) they cannot occur…
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