CUET UG 2025 — Mathematics Algebra

$$P(A') = 1 - P(A)$$P(A′)=1−P(A)

This is the complement rule.

$$(A) \to (III)$$(A)→(III)

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$$P(\phi) = 0$$P(ϕ)=0

$\phi$ϕ is the empty set (no outcome), so the probability is always 0.

$$(B) \to (IV)$$(B)→(IV)

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$$P(A|B) = \dfrac{P(A \cap B)}{P(B)};\ P(B) \neq 0$$P(A∣B)=P(B)P(A∩B)​; P(B)=0

In $P(A|B)$P(A∣B), the event after the bar (here $B$B) goes in the denominator.

$$(C) \to (II)$$(C)→(II)

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$$P(B|A) = \dfrac{P(A \cap B)}{P(A)};\ P(A) \neq 0$$P(B∣A)=P(A)P(A∩B)​; P(A)=0

In $P(B|A)$P(B∣A), the event after the bar (here $A$A) goes in the denominator.

$$(D) \to (I)$$(D)→(I)

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$$(A) \to (III),\quad (B) \to (IV),\quad (C) \to (II),\quad (D) \to (I)$$(A)→(III),(B)→(IV),(C)→(II),(D)→(I)