GATE Overflow for GATE IN - Questions without answers in Probability and Statistics

GATE IN 2026 | Question: 21

Mon, 23 Feb 2026 13:37:20 +0000

A data set is given to be $[1,2,0,-1,-3,1,2,0,1]$.

The median of the data set is $\_\_\_\_$ . (rounded off to the nearest integer)

GATE IN 2026 | Question: 26

Mon, 23 Feb 2026 13:37:17 +0000

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is $\_\_\_\_$.

$\dfrac{3}{5}$
$\dfrac{3}{20}$
$\dfrac{3}{10}$
$\dfrac{2}{5}$

GATE IN 2025 | Question: 42

Thu, 06 Mar 2025 17:17:22 +0000

The probability of a student missing a class is $0.1$. In a total number of $10$ classes, the probability that the student will not miss more than one class is ___________ (rounded off to two decimal places).

GATE IN 2024 | Question: 25

Fri, 16 Feb 2024 18:41:00 +0000

Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have red logo jerseys. Five teams of Pool-B have blue logo jerseys while the rest three have red logo jerseys.

If one team from each pool reaches the final, the probability that one team has a blue logo jersey and another has a red logo jersey is $\_\_\_\_\_\_$ (rounded off to one decimal place).

GATE IN 2024 | Question: 40

Fri, 16 Feb 2024 18:40:56 +0000

The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient of determination, $R^{2}= \_\_\_\_\_\_$(rounded off to three decimal places).

$\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline y (\text{psig}) & 10.3 & 10.5 & 10.4 & 10.5 & 10.5 \\ \hline \end{array}$

GATE IN 2024 | Question: 55

Fri, 16 Feb 2024 18:40:52 +0000

A random variable $X$ has a probability density function

$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$

The probability of $X>2$ is $\_\_\_\_\_$ (rounded off to three decimal places).

GATE IN 2023 | Question: 22

Mon, 22 May 2023 00:14:39 +0000

$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, the value of $E[X]-E\left[X^{2}\right]$ is_____________(rounded off to one decimal place).

GATE IN 2023 | Question: 43

Mon, 22 May 2023 00:14:17 +0000

Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The sample standard deviation of the measurement ___________is $\mathrm{kg}$ (rounded off to two decimal places).

GATE IN 2022 | Question: 22

Sun, 20 Mar 2022 17:33:58 +0000

A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is ____________ (round off to two decimal places)

GATE IN 2021 | Question: 37

Fri, 19 Feb 2021 15:48:36 +0000

Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\left ( 1,4 \right )$. Then $P\left ( Y\leq X \right )$ is equal to __________________ (rounded off to two decimal places).

GATE2020 IN: 32

Tue, 03 Nov 2020 14:26:43 +0000

Consider two identical bags $B1$ and $B2$ each containing $10$ balls of identical shapes and sizes. Bag $B1$ contains $7$ Red and $3$ Green balls, while bag $B2$ contains $3$ Red and $7$ Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag $B1$ $\text{(rounded off to one decimal place)}$ is ______.

GATE2020: 16

Tue, 03 Nov 2020 04:24:36 +0000

A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt $\text{(rounded off to two decimal places)}$ is __________

GATE IN 2017 | Question: 26

Mon, 02 Nov 2020 00:00:21 +0000

The probability that a communication system will have high fidelity is $0.81$. The probability that the system will have both high fidelity and high selectivity is $0.18$. The probability that a given system with high fidelity will have high selectivity is

$0.181$
$0.191$
$0.222$
$0.826$

GATE2019 IN: 3

Sun, 10 Feb 2019 14:41:24 +0000

A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is

4/15
7/16
½
8/15

GATE2019 IN: 27

Sun, 10 Feb 2019 14:41:22 +0000

The function p(x) is given by p(x) = A/x$^\mu$ where A and $\mu$ are constants with $\mu$ > 1 and 1 $\le$ x <$\infty$ and p(x) = 0 for -$\infty$ < x <1. For p(x) to be a probability density function, the value of A should be equal to

$\mu$ – 1
$\mu$ + 1
1/($\mu$ – 1)
1/($\mu$ +1)

GATE2016-3

Mon, 26 Mar 2018 18:43:25 +0000

A voltage $V_1$ is measured $100$ times and its average and standard deviation are $100$ V and $1.5$ V respectively. A second voltage $V_2$, which is independent of $V_1$, is measured $200$ times and its average and standard deviation are $150$ V and $2$ V respectively. $V_3$ is computed as: $V_3$=$V_1$+$V_2$. Then the standard deviation of $V_3$ in volt is_____.

GATE2016-27

Mon, 26 Mar 2018 18:43:22 +0000

An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same color. The probability of getting a red ball in the next draw is

$\frac{65}{156}$
$\frac{67}{156}$
$\frac{79}{156}$
$\frac{89}{156}$

GATE2015-36

Mon, 26 Mar 2018 18:32:00 +0000

The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ are defective is

0.001
0.057
0.107
0.3

GATE2015-37

Mon, 26 Mar 2018 18:31:59 +0000

The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}$ is __________ .

GATE2014-2

Sun, 25 Mar 2018 23:10:51 +0000

Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________.

GATE2014-5

Sun, 25 Mar 2018 23:10:51 +0000

The figure shows the schematic of a production process with machines $A, B$ and $C$. An input job needs to be pre-processed either by $A$ or by $B$ before it is fed to $C$, from which the final finished product comes out. The probabilities of failure of the machines are given as:

$$P_A=0.15, P_B=0.05, P_C=0.1$$

Assuming independence of failures of the machines, the probability that a given job is successfully processed (up to the third decimal place) is ________.

GATE IN 2013 | Question: 47

Sun, 25 Mar 2018 19:30:35 +0000

Two ammeters $A_1$ and $A_2$ measure the same current and provide readings $I_1$ and $I_2,$ respectively. The ammeter errors can be characterized as independent zero mean Gaussian random variables of standard deviations $\sigma_1$ and $\sigma_2$, respectively. The value of the current is computed as :

$I=\mu I_1+(1-\mu)I_2$

The value of $\mu$ which gives the lowest standard deviation of $I$ is

$\frac{\sigma^2_2}{\sigma_1^2+\sigma_2^2}$
$\frac{\sigma_1^2}{\sigma_1^2+\sigma_2^2}$
$\frac{\sigma_2}{\sigma_1+\sigma_2}$
$\frac{\sigma_1}{\sigma_1+\sigma_2}$

GATE IN 2013 | Question: 16

Sun, 25 Mar 2018 19:30:31 +0000

A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is

$0.368$
$0.5$
$0.632$
$1.0$

GATE IN 2012 | Question: 26

Sun, 25 Mar 2018 09:53:04 +0000

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

$1/3$
$1/2$
$2/3$
$3/4$

GATE IN 2012 | Question: 3

Sun, 25 Mar 2018 09:53:00 +0000

Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$ is

$3/4$
$9/16$
$1/4$
$2/3$

GATE2018IN: 27

Tue, 20 Feb 2018 12:03:44 +0000

Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

GATE2018IN: 5

Tue, 20 Feb 2018 12:03:42 +0000

Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is

$\frac{5}{16}$
$\frac{3}{16}$
$\frac{3}{5}$
$\frac{9}{16}$

GATE2018IN: 3

Tue, 20 Feb 2018 12:03:41 +0000

X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is