WBJEE · Maths · Probability
\(A, B, C\) are mutually exclusive events such that \(P(A)=\frac{3 x+1}{3}, P(B)=\frac{1-x}{4}\) and \(P(C)=\frac{1-2 x}{2}\). Then the set of possible values of \(\mathrm{x}\) are in
- A \([0,1]\)
- B \(\left[\frac{1}{3}, \frac{1}{2}\right]\)
- C \(\left[\frac{1}{3}, \frac{2}{3}\right]\)
- D \(\left[\frac{1}{3}, \frac{13}{3}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[\frac{1}{3}, \frac{1}{2}\right]\)
Step-by-step Solution
Detailed explanation
\(0 \leq \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})+\mathrm{P}(\mathrm{C}) \leq 1\) and \(0 \leq \mathrm{P}(\mathrm{A}) \leq 1,0 \leq \mathrm{P}(\mathrm{B}) \leq 1,0 \leq \mathrm{P}(\mathrm{C}) \leq 1 \Rightarrow \frac{1}{3} \leq \mathrm{x} \leq \frac{1}{2}\)
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