Probability Question 6
Question: The probabilities of two events A and B are given as $ P(A)=0.8 $ and $ P(B)=0.7. $ What is the minimum value of $ P(A\cap B)? $
Options:
A) 0
B) 0.1
C) 0.5
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
As we know $ P(A\cup B)\le 1 $
$ \therefore P(A)+P(B)-P(A\cap B)\le 1 $
$ \Rightarrow 0.8+0.7-P(A\cap B)\le 1 $
$ \Rightarrow P(A\cap B)\ge 1.5-1 $
$ \Rightarrow P(A\cap B)\ge 0.5 $
Hence, the minimum value of $ P(A\cap B) $ is 0.5.
BETA
