AP EAMCET · Maths · Probability
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 ____
- A Always true
- B Always false
- C Not true in some examples
- D True only in some cases
Answer & Solution
Correct Answer
(A) Always true
Step-by-step Solution
Detailed explanation
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.
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