In reference to Inferential Statistics, if… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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In reference to Inferential Statistics, if $\bar{x}$ is a sample mean of random data $\{x_i\}_{i=1}^n$ and $n$ is the sample size, then the formula $\displaystyle \frac{1}{n-1}\sum_{i=0}^n(x_i - \bar{x})^2$ represents

Official previous-year question

Held on 30 May 2025 · Verified 13 Jul 2026.

Options

A
Mean
B
Variance
C
Standard Deviation
D
t-Statistic

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Solution

The probability of Nitin getting grade A in Mathematics or Physics (or both) needs to be found.

Given:
P(A in Math) = 0.2
P(A in Physics) = 0.3
P(A in Chemistry) = 0.9
All events are independent.

For the probability of "A OR B":

P(A or B) = P(A) + P(B) - P(A and B)

The term P(A and B) is subtracted because when adding P(A) + P(B), the case where both happen is counted twice.

Since the events are independent:

P(Math AND Physics) = P(Math) × P(Physics)

P(Math AND Physics) = 0.2 × 0.3

P(Math AND Physics) = 0.06

P(Math OR Physics) = P(Math) + P(Physics) - P(Math AND Physics)

P(Math OR Physics) = 0.2 + 0.3 - 0.06

P(Math OR Physics) = 0.5 - 0.06

P(Math OR Physics) = 0.44

Therefore, the probability of getting A grade in either Mathematics or Physics is $0.44$ .

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