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UPSC NDA I 2024 Mathematics Paper

Question Numbers: 111-112

Consider the following for the items that follow:

Let A and B be two events such that P(A ∪ B) ≥ 0.75 and 0.125 ≤ P(A ∩ B) ≤ 0.375.

Question : 112 of 120

Marks: +1, -0

What is the maximum value of P(A) + P(B) ?

Solution:

Concept:

Use the formula:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Explanation:

Given

P(A \cup B) = 0.75

and

0.125 \le P(A \cap B) \le 0.375

From the formula,

P(A) + P(B) = P(A \cup B) + P(A \cap B)

To maximize

P(A)+P(B)

, we use the largest possible

P(A \cap B)

, which is

0.375

Thus

P(A)+P(B)_{\text{max}} = 0.75 + 0.375 = 1.125

Answer:

1.125

(Option B).

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