Statistics And Probability Question 581
Question: If $ P(A)=P(B)=x $ and $ P(A\cap B)=P({A}’\cap {B}’)=\frac{1}{3} $ , then $ x= $
[UPSEAT 2003]
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{3} $
C) $ \frac{1}{4} $
D) $ \frac{1}{6} $
Show Answer
Answer:
Correct Answer: A
Solution:
-
$ P(A'\cap B')=1-P(A\cup B)\Rightarrow \,P(A\cup \,B)=\frac{2}{3} $ Now $ P(A\cup B)\,=P(A)+P(B)-P(A\cap B) $
Þ $ \frac{2}{3}=x+x-\frac{1}{3}\Rightarrow ,x=\frac{1}{2} $ .
BETA
