Question

Suppose $A,B$ be two events such that $P(A)=0.9$ and $P(B)=0.8$ and $P(A\cap B)\ge 0.7$. Then we can conclude that such a case is_______

• A. Always true
• B. Always false
• C. Not true in some examples
• D. True only in some case

Answer 1

Answer: (A)

Maximum value of probability of $A$ or $B$ is,
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$=0.9+0.8-0.7=1$
Which is probability of a sure event.
As all other values of $P(A\cup B)$ are less than $1.$ so this is always true.