If S is the sample space and P(A) = 1 3 P(B) and S = A where A and B are two mutually exclusive events, then P (A) =

If S is the sample space and P(A) = 1 3 P(B) and S = A where A an…

MCQ

If $S$ is the sample space and $ \text{P(A)} = \frac{1}{3} \text{P(B)}$ and $\text{S} = \text{A}\cup\text{B}$ where $A$ and $B$ are two mutually exclusive events, then $P (A) =$

✓
$\frac{1}{4}$
B
$\frac{1}{2}$
C
$\frac{3}{4}$
D
$\frac{3}{8}$

✓

Answer

Correct option: A.

$\frac{1}{4}$

Let $\text{P(B)}=\text{P}$
Than $\text{P(A)}=\frac{1}{3}\text{P}$
Since $A$ and $B$ are two mutually exclusive events, we have :
$\text{A}\cup\text{B}=\text{S}$
$\Rightarrow\text{P}\text{(A}\cup\text{B)}=\text{P}\text{(S)}$
$\Rightarrow\text{P}\text{(A}\cup\text{B)}=1$
$\Rightarrow\text{P}\text{(A)}+\text{(B)}=1$
$\Rightarrow\frac{1}{2}\text{P}+\text{P}=1$
$\Rightarrow\frac{4\text{p}}{3}=1$
$\therefore\text{P(A)}=\frac{1}{3}\text{P}$
$=\frac{1}{3}\times\frac{3}{4}=\frac{1}{4}$

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