CUET UG 2025 — Mathematics Algebra

Given $P(A) = 0.8$P(A)=0.8, $P(B) = 0.5$P(B)=0.5, $P(B|A) = 0.4$P(B∣A)=0.4

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(A) $P(A \cap B)$P(A∩B)

$$P(B|A) = \dfrac{P(A \cap B)}{P(A)}$$P(B∣A)=P(A)P(A∩B)​

$$P(A \cap B) = P(B|A) \times P(A)$$P(A∩B)=P(B∣A)×P(A)

$$= 0.4 \times 0.8$$=0.4×0.8

$$= 0.32 \longrightarrow \text{(II)}$$=0.32⟶(II)

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(B) $P(A|B)$P(A∣B)

$$P(A|B) = \dfrac{P(A \cap B)}{P(B)}$$P(A∣B)=P(B)P(A∩B)​

$$= \dfrac{0.32}{0.5}$$=0.50.32​

$$= 0.64 \longrightarrow \text{(III)}$$=0.64⟶(III)

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(C) $P(A \cup B)$P(A∪B)

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$P(A∪B)=P(A)+P(B)−P(A∩B)

$$= 0.8 + 0.5 - 0.32$$=0.8+0.5−0.32

$$= 0.98 \longrightarrow \text{(IV)}$$=0.98⟶(IV)

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(D) $P(A')$P(A′)

$$P(A') = 1 - P(A)$$P(A′)=1−P(A)

$$= 1 - 0.8$$=1−0.8

$$= 0.2 \longrightarrow \text{(I)}$$=0.2⟶(I)

Therefore, the correct answer is (A)-(II), (B)-(III), (C)-(IV), (D)-(I).