Probability Question 248
Question: The probability of happening at least one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then $ P(\bar{A})+P(\bar{B})= $
[Roorkee 1989; IIT 1987; MP PET 1997; DCE 2001; J & K 2005]
Options:
A) 0.4
B) 0.8
C) 1.2
D) 1.4
Show Answer
Answer:
Correct Answer: C
Solution:
We are given that $ P(A\cup B)=0.6 $ and $ P(A\cap B)=0.2 $ .
We know that if $ A $ and $ B $ are any two events, then $ P(A\cup B)=P(A)+P(B)-P(A\cap B) $
$ 0.6=1-P(\bar{A})+1-P(\bar{B})-0.2 $
$ \Rightarrow P(\bar{A})+P(\bar{B})=2-0.8=1.2 $ .
BETA
