What is the <strong>MINIMUM</strong> value of P(A)+P(B)?
Consider the following for the next two (02) items that follow : Let A and B be two events such that P(A\cup B)\geq 0.75 and 0.125\leq P(A\cap B)\leq 0.375.
- A. 0.625
- B. 0.750
- C. 0.825
- D. 0.875 ✓
Correct Answer: D. 0.875
Explanation
We know the addition theorem of probability: P(A \cup B) = P(A) + P(B) - P(A \cap B), which gives P(A) + P(B) = P(A \cup B) + P(A \cap B). To minimize the sum P(A) + P(B), we take the minimum possible values of both terms on the right side. The minimum of P(A \cup B) is 0.75 and the minimum of P(A \cap B) is 0.125. Therefore, the minimum value of P(A) + P(B) is 0.75 + 0.125 = 0.875.
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