Question

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

 

पर्याय

•  1/4

• 1/2

• 3/4

•  3/8

   

Answer 1

 1/4

Let P(B) = p
Then P(A) = \[\frac{1}{3}p\] 

Since A and B are two mutually exclusive events, we have:
A ∪ B = S
⇒ P (A∪B) = P (S)
⇒ P (A∪B) = 1
⇒ P (A) + P (B) = 1
⇒ \[\frac{1}{3}p + p = 1\]

\[\Rightarrow \frac{4p}{3} = 1\]
\[ \Rightarrow p = \frac{3}{4}\]

∴ P (A) = \[\frac{1}{3}p = \frac{1}{3} \times \frac{3}{4} = \frac{1}{4}\]