TS EAMCET · Maths · Probability
If \(A, B, C\) are three events of a sample space such that \(P(B)=\frac{3}{2} P(A)\) and \(P(C)=\frac{1}{2} P(B)\) then which of the following is correct?
- A \(P(A \cup C)=\frac{7}{13}\) when \(A, B, C\) are exhaustive and mutually exclusive events
- B \(\frac{10}{13} \leq P(B \cup C) \leq 1\) when \(A, B, C\) are exclusive events
- C \(P(C)=\frac{7}{13}\) when, \(A, B, C\) are exhaustive events
- D \(P(A \cup B \cup C)=P(A) P(B) P(C)\)
Answer & Solution
Correct Answer
(A) \(P(A \cup C)=\frac{7}{13}\) when \(A, B, C\) are exhaustive and mutually exclusive events
Step-by-step Solution
Detailed explanation
Let \(P(B)=x\) Then, \(P(A)=\frac{2}{3} x\) and \(P(C)=\frac{1}{2} x\) Now, if \(A, B, C\) are exhaustive and mutually exclusive, then \(P(A \cup B \cup C)=1\),…
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