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# An experiment can result in only 3 mutually exclusive events A,B and C. If $P(A) = 2P(B) = 3P(C)$ then $P(A) =$

$\begin {array} {1 1} (A)\;\large\frac{6}{11} & \quad (B)\;\large\frac{5}{11} \\ (C)\;\large\frac{9}{11} & \quad (D)\;None\: of \: these \end {array}$

Let $P(A) = a$
$P(B) = b$
$P(C) = c$
then $a + b + c=1$
Given $\rightarrow a = 2b = 3c$
$\Rightarrow C = \large\frac{a}{3}\: \: b = \large\frac{a}{2}$
putting the value of b and c in the equation $a+b+c=1$
$\Rightarrow a + \large\frac{a}{2}+ \large\frac{a}{3}=1$
$\large\frac{6a+3a+2a}{6}=1$
$11a=6$
$a = \large\frac{6}{11}$
Ans : (A)