Question

Events A, B, C are mutually exclusive events such that $P(A)=\frac{3x+1}{3},\ P(B)=\frac{1-x}{4}\ and\ P(C)=\frac{1-2x}{2}$. The set of possible values of x are in the interval.
(a) [0 , 1]
(b) $\bigg [\frac{1}{3},\frac{1}{2}\bigg]$
(c) $\bigg [\frac{1}{3},\frac{2}{3}\bigg]$
(d) $\bigg [\frac{1}{3},\frac{13}{3}\bigg]$

Answer 1

(a) [0 , 1]

(b) $\bigg [\frac{1}{3},\frac{1}{2}\bigg]$

(c) $\bigg [\frac{1}{3},\frac{2}{3}\bigg]$

(d) $\bigg [\frac{1}{3},\frac{13}{3}\bigg]$