IGDTUW 2025 — Mathematics PYQ

Solution

The expression $P(A^{\prime }\cap B^{\prime })+P(A^{\prime }\cap B)+P(A\cap B^{\prime })$ represents every region in the sample space except the intersection $P(A\cap B)$.

$P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.5+0.7-0.3=0.9$.

$P(A^{\prime }\cap B^{\prime })=1-P(A\cup B)=1-0.9=0.1$.

$P(A^{\prime }\cap B)=P(B)-P(A\cap B)=0.7-0.3=0.4$.

$P(A\cap B^{\prime })=P(A)-P(A\cap B)=0.5-0.3=0.2$.

Sum $=0.1+0.4+0.2=0.7$.

Correct Option: (b)