Q74 / 160 · AP EAMCET 2015 · Mathematics

If $\frac{1+3 P}{3}, \frac{1-2 P}{2}$ are probabilities of two mutually exclusive events, then $P$ lies in the interval.

  • Correct answer
    A
    $\left[-\frac{1}{3}, \frac{1}{2}\right]$
  • B
    $\left(\frac{-1}{2}, \frac{1}{2}\right)$
  • C
    $\left[-\frac{1}{3}, \frac{2}{3}\right]$
  • D
    $\left(\frac{-1}{3}, \frac{2}{3}\right)$

Solution

Given, $\begin{aligned} & 0 \leq \frac{1+3 P}{3} \leq 1 \text { and } 0 \leq \frac{1-2 P}{3} \leq 1 \\ & \Rightarrow \quad 0 \leq 1+3 P \leq 3 \text { and } 0 \leq 1-2 P \leq 2 \\ & \Rightarrow \quad-1 \leq 3 P \leq 2 \text { and }-1 \leq-2 P \leq 1 \\ & \Rightarrow \quad-\frac{1}{3} \leq P \leq \frac{2}{3} \text { and }-\frac{1}{2} \leq P \leq \frac{1}{2} \\ & \therefore \quad P \in\left[-\frac{1}{3}, \frac{1}{2}\right] \end{aligned}$

Hence, the correct answer is option: 'A'.

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