Q. If $\left( \ \frac{1 + a}{3} \right)\ and\ \left( \ \frac{1 - a}{4} \right)$ are probability of two mutually exclusive events, then set of all values of $a$ is
A) $- 1 \leq a \leq 1$
B) $- 7 \leq a \leq 5$
C) $- 1 \leq a \leq 2$
D) $- 4 \leq a \leq 1$
Explanation
(a)
Since, $0 \leq \frac{1 + a}{3} \leq 1\ \Rightarrow \ - 1 \leq a \leq 2$ …(i)
and $0 \leq \frac{1 - a}{4} \leq 1\ \Rightarrow \ - 3 \leq a \leq 1$ …(ii)
Also, as $\frac{1 + a}{3}$ and $\frac{1 - a}{4}\$ are the probabilities of two mutually exclusive events.
$\therefore 0 \leq \frac{1 + a}{3} + \frac{1 - a}{4} \leq 1\ \Rightarrow \ - 7 \leq a \leq 5$ …(iii)
From relations (i), (ii) and (iii), we get
$- 1 \leq a \leq 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.