CUET UG 2025 — Mathematics Arithmetic

Given: $P(A) = 0.3$P(A)=0.3, $P(B) = 0.4$P(B)=0.4, and $A$A and $B$B are independent events.

For independent events, $P(A \cap B) = P(A) \times P(B)$P(A∩B)=P(A)×P(B).

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For (A) $P(A \cap B)$P(A∩B):

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

$$P(A \cap B) = 0.3 \times 0.4$$P(A∩B)=0.3×0.4

$$P(A \cap B) = 0.12$$P(A∩B)=0.12

(A) matches with (III). We know enough—can mark the option right away and save time!

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For (B) $P(A \cup B)$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)

$$P(A \cup B) = 0.3 + 0.4 - 0.12$$P(A∪B)=0.3+0.4−0.12

$$P(A \cup B) = 0.58$$P(A∪B)=0.58

(B) matches with (IV)

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For (C) $P(A|B)$P(A∣B):

Since $A$A and $B$B are independent, $P(A|B) = P(A)$P(A∣B)=P(A).

$$P(A|B) = 0.3$$P(A∣B)=0.3

(C) matches with (I)

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For (D) $P(B|A)$P(B∣A):

Since $A$A and $B$B are independent, $P(B|A) = P(B)$P(B∣A)=P(B).

$$P(B|A) = 0.4$$P(B∣A)=0.4

(D) matches with (II)

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