Probability Question 174
Question: For two events A and B, if $ P(A)=P( \frac{A}{B} )=\frac{1}{4} $ and $ P( \frac{B}{A} )=\frac{1}{2}, $ then
Options:
A) A and B are independent
B) $ P( \frac{{{A}’}}{B} )=\frac{3}{4} $
C) $ P( \frac{{{B}’}}{{{A}’}} )=\frac{1}{2} $
D) All of the above
Show Answer
Answer:
Correct Answer: D
Solution:
$ A,B $ are independent as $ P(A)=P( \frac{A}{B} ) $
$ P( \frac{{{A}’}}{B} )=1-\frac{1}{4}=\frac{3}{4} $ as $ A,B $ are independent
$ \Rightarrow {A}’,B $ are independent.
$ P( \frac{{{B}’}}{{{A}’}} )=P({B}’)=1-\frac{1}{2}=\frac{1}{2}. $
BETA
