NDA 1 2024 Maths, question 112

Topic: Probability

Passage · Q111 to Q112

Let $A$ and $B$ be two events such that $P(A\cup B)\ge 0.75$ and $0.125\le P(A\cap B)\le 0.375$ .

Q112

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

(a) $0.75$
(b) $1.125$
(c) $1.375$ Correct answer
(d) $1.625$

Solution.

Answer: (c) $1.375$

A union probability cannot exceed 1 and the intersection is at most 0.375.
Thus P(A) + P(B) ≤ 1.375.
Equality is feasible: intersection 0.375 and the two exclusive parts summing to 0.625.
Hence the maximum is 1.375.