Probability Question 172
Question: If A and B are two independent events such that $ P(A)=\frac{1}{2},P(B)=\frac{1}{5}, $ then
Options:
A) $ P( \frac{A}{B} )=\frac{1}{2} $
B) $ P( \frac{A}{A\cup B} )=\frac{5}{6} $
C) $ P( \frac{A\cap B}{{A}’\cup {B}’} )=0 $
D) All of the above
Show Answer
Answer:
Correct Answer: D
Solution:
$ P(A/B)=P(A) $ as independent event $ =\frac{1}{2}. $
$ P{A/(A\cup B)}=\frac{P[A\cap (A\cup B)]}{P(A\cup B)} $
Since $ A\cap (A\cup B)=A\cap [A-B-A\cap B] $ = $A - A\cap B - A\cap B = a $
$ \Rightarrow P( \frac{A}{A\cup B} )=\frac{P(A)}{P(A\cup B)}=\frac{\frac{1}{2}}{\frac{1}{2}-\frac{1}{5}-\frac{1}{10}}=\frac{\frac{1}{2}}{\frac{6}{10}}=\frac{5}{6} $ and similarly $ P( \frac{A\cap B}{{A}’\cup {B}’} ) $ .
BETA
