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,…
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 ____
Always true
Always false
Not true in some examples
True only in some cases
Solution
Maximum value of probability of \(A\) or \(B\) is,
\(\begin{aligned}
P(A \cup B) & =P(A)+P(B)-P(A \cap B) \\
& =0.9+0.8-0.7=1
\end{aligned}\)
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.