Statistics And Probability Question 44
Question: If $ E_1 $ and $ E_2 $ are two events such that $ P(E_1)=1/4,P(E_2/E_1)=1/2 $ and $ P(E_1/E_2)=1/4 $ , then choose the incorrect statement.
Options:
A) $ E_1andE_2 $ are independent
B) $ E_1 $ and $ E_2 $ are exhaustive
C) $ E_2 $ is twice as likely to occur as $ E_1 $
D) Probabilities of the events $ E_1\cap E_2 $ , $ E_1 $ and $ E_2 $ are in GP.
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ P(E_2/E_1)=\frac{P(E_1\cap E_2)}{P(E_1)} $
$ \Rightarrow \frac{1}{2}=\frac{P(E_1\cap E_2)}{1/4}\Rightarrow P(E_1\cap E_2)=\frac{1}{8} $ $ =P(E_2).P(E_1/E_2)=P(E_2).\frac{1}{4} $
$ \Rightarrow P(E_2)=\frac{1}{2}\sin ceP(E_1\cap E_2) $ $ =\frac{1}{8}=P(E_1).P(E_2) $
$ \Rightarrow $ Events are independent Also $ P(E_1\cup E_2)=\frac{1}{2}+\frac{1}{4}-\frac{1}{8}=\frac{5}{8} $
$ \Rightarrow E_1\And E_2 $ are non-exhaustive
BETA
