Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If A, B, C Are Three Mutually Exclusive and Exhaustive Events of an Experiment Such that 3 P(A) = 2 P(B) = P(C), Then P(A) is Equal to - Mathematics

MCQ

If ABC are three mutually exclusive and exhaustive events of an experiment such that 3 P(A) = 2 P(B) = P(C), then P(A) is equal to

#### Options

•  $\frac{1}{11}$

•  $\frac{2}{11}$

•   $\frac{5}{11}$

•  $\frac{6}{11}$

#### Solution

Let 3 P(A) = 2 P(B) = P(C) = p. Then,
P(A) = $\frac{p}{3}$, P(B) =$\frac{p}{2}$ and P(C) = p

It is given that ABC are three mutually exclusive and exhaustive events.

∴ P(A) + P(B) + P(C) = 1                               [P(A ∩ B) = P(B ∩ C) = P(C ∩ A) = P(A ∩ B ∩ C) = 0 and P(A ∪ B ∪ C) = 1]
$\Rightarrow \frac{p}{3} + \frac{p}{2} + p = 1$
$\Rightarrow \frac{11p}{6} = 1$
$\Rightarrow p = \frac{6}{11}$
$\therefore P\left( A \right) = \frac{p}{3} = \frac{\frac{6}{11}}{3} = \frac{2}{11}$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 33 | Page 73