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  4. Suppose A, B be two events such that P(A)=0.9 and P(B)=0.8 and P(A ∩ B) ≥ 0.7. Then we can conclude that such a case is

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

AP EAMCETAP EAMCET 2020

Solution:

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.