Statistics and Probability

Comprehensive Question Bank & Study Notes

Multiple Choice Questions

1 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 28th January Morning Shift
#993
Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denote the number of defective oranges, then the variance of $x$ is
(A) 26/75
(B) 14/25
(C) 18/25
(D) 28/75
EASY
2 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 28th January Morning Shift
#992
Two number $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1} + i^{k_2}$, ($i = \sqrt{-1}$) is non-zero, equals
(A) $\frac{3}{4}$
(B) $\frac{1}{2}$
(C) $\frac{1}{4}$
(D) $\frac{2}{3}$
EASY
3 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 28th January Evening Shift
#991
Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:
(A) $\frac{1}{4}$
(B) $\frac{1}{2}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$
EASY
4 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 28th January Evening Shift
#990
Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and Bag $B_3$ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag $B_2$ is:
(A) $\frac{2}{5}$
(B) $\frac{4}{15}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$
EASY
5 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 29th January Evening Shift
#989
Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is $\frac{29}{45}$, then n is equal to:
(A) 5
(B) 6
(C) 4
(D) 3
EASY
6 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 2nd April Evening Shift
#988
Given three indentical bags each containing $10$ balls, whose colours are as follows:

| | Red | Blue | Green |
|--------|-----|------|-------|
| Bag I | $3$ | $2$ | $5$ |
| Bag II | $4$ | $3$ | $3$ |
| Bag III| $5$ | $1$ | $4$ |

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is $p$ and if the ball is Green, the probability that it is from bag III is $q$, then the value of $(\frac{1}{p} + \frac{1}{q})$ is:
(A) $6$
(B) $9$
(C) $7$
(D) $8$
EASY
7 Competency APPLY MCQ_SINGLE 4 Mark(s) 2025 JEE Main 2025 (Online) 4th April Morning Shift
#986
A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is
(A) $\frac{11}{15}$
(B) $\frac{2}{15}$
(C) $\frac{3}{5}$
(D) $\frac{28}{75}$
HARD
8 Knowledge REMEMBER MCQ_SINGLE 1 Mark(s)
#705
MEDIUM