Q28 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Probability

An experiment yields $3$ mutually exclusive and exhaustive events $A, B$ and $C$ $.$ If $P (A) = 2 P (B) = 3 P (C),$ then $P (A)$ is equal to

A
$\frac{1}{11}$
B
$\frac{2}{11}$
C
$\frac{3}{11}$
Correct answer
D
$\frac{6}{11}$

Solution

Given, events

A, B

and

C

are mutually exclusive and exhaustive, hence

P (A \cup B \cup C) = 1

\Rightarrow P (A) + P (B) + P (C) = 1

\Rightarrow P (A) + \frac{1}{2} P (A) + \frac{1}{3} P (A) = 1

\Rightarrow \frac{11}{6} P (A) = 1

\Rightarrow P (A) = \frac{6}{11}

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

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