UPSC NDA I 2024 Mathematics Paper

We know that:
P(A∪B)=P(A)+P(B)−P(A∩B)
Therefore:
P(A)+P(B)=P(A∪B)+P(A∩B)
To maximize P(A)+P(B), we need to maximize both P(A∪B) and P(A∩B).
The maximum value of P(A∪B) is given as 0.75 . The maximum value of P(A∩B) is 0.375 .
Therefore, the maximum value of P(A)+P(B) is:
0.75+0.375=1.125