NIMCET 2025 — Mathematics PYQ

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Question

NIMCET 2025 — Mathematics PYQ

NIMCET | Mathematics | 2025

Consider the sample space $\Omega = \{ (x,y) : x, y \in \{ 1, 2, 3, 4\} \}$ where each outcome is equally likely. Let $A = \{x \geq 2\}$ and $B = \{y > x\}$ be two events. Then which of the following is NOT true?

Choose the correct answer:

Explanation

Solution

Total Outcomes:

n(\Omega) = 4 \times 4 = 16

Event $A$ ( $x \in \{2, 3, 4\}$ ):

n(A) = 3 \times 4 = 12

P(A) = \frac{12}{16} = \frac{3}{4}

Event $B$ ( $y > x$ ):

Outcomes: $(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)$

n(B) = 6

P(B) = \frac{6}{16} = \frac{3}{8}

Event $A \cap B$ ( $x \geq 2$ AND $y > x$ ):

Outcomes: $(2,3), (2,4), (3,4)$

n(A \cap B) = 3

P(A \cap B) = \frac{3}{16}

Comparison:

Calculated $P(A \cap B) = \frac{3}{16}$

Given in Option (C) $P(A \cap B) = \frac{1}{4} = \frac{4}{16}$

\frac{3}{16} \neq \frac{4}{16}

Final Answer:

The statement in (A) is NOT true.