Probability Question 260
Question: If A and B are two events such that $ P(A\cup B)+P(A\cap B)=\frac{7}{8} $ and $ P(A)=2P(B), $ then $ P(A)= $
Options:
A) $ \frac{7}{12} $
B) $ \frac{7}{24} $
C) $ \frac{5}{12} $
D) $ \frac{17}{24} $
Show Answer
Answer:
Correct Answer: A
Solution:
Since we have $ P(A\cup B)+P(A\cap B)=P(A)+P(B) $
$ =P(A)+\frac{P(A)}{2} $
$ \Rightarrow \frac{7}{8}=\frac{3P(A)}{2}\Rightarrow P(A)=\frac{7}{12}. $
BETA
