Statistics And Probability Question 51
Question: Let A and B be two events such that $ P(A\cap B’)=0.20,P(A’\cap B)=0.15, $ $ P(A’\cap B’)=0.1, $ Then $ P(A/B) $ is equal to
Options:
A) 11/14
B) 2/11
C) 2/7
D) 1/7
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ P(A\cap B’)=P(A)-P(A\cap B)=0.20 $ Also, $ P(A’\cap B)=P(B)-P(A\cap B)=0.15 $
$ \Rightarrow P(A)+P(B)-2P(A-B)=0.35 $ Now, $ P(A’\cap B’)=1-P(A\cup B) $
$ \Rightarrow 0.1=1-P(A)-P(B)+P(A\cap B) $
$ \Rightarrow P(A)+P(B)-P(A\cap B)=0.9 $
$ \Rightarrow P(A\cap B)=0.9-0.35=0.55 $ and $ P(A)=0.75,P(B)=0.70 $ Now, $ P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{0.55}{0.70} $
BETA
