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Recent questions and answers in Probability and Statistics

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GATE Mechanical 2026 | Question: 29
A student council of $10$ members consists of two students from engineering school, three students from science school and five students from arts school. The university ...
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604
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GATE Mechanical 2021 Set 1 | Question: 35
Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each ac...
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277
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GATE Mechanical 2025 | Question: 4
If two unbiased coins are tossed, then what is the probability of having at least one head?$0.25$$0.5$$0.675$$0.75$
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412
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GATE Mechanical 2025 | Question: 27
​​​​​​Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, arePer...
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501
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GATE2018-1-18
A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is$33.3$$3.33$$0.33$$0.0033$
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727
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GATE ME 2012 | Question: 45
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected...
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538
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GATE Mechanical 2024 | Question: 25
​​​​​A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson dist...
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365
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GATE Mechanical 2024 | Question: 34
Let $\text{X}$ be a continuous random variable defined on $[0,1]$ such that its probability density function $f(x)=1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y=\log...
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GATE Mechanical 2023 | Question: 1
A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the mac...
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341
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GATE Mechanical 2022 Set 1 | Question: 37
Let a random variable $X$ follow Poisson distribution such that $$\text{Prob (X = 1) = Prob (X = 2)}$$. The value of $\text{Prob (X = 3)}$ is ______________ (round off t...
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629
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GATE Mechanical 2021 Set 2 | Question: 3
The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are$\sqrt{np},np\left ( 1-2p \right )$$...
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440
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GATE Mechanical 2021 Set 2 | Question: 8
A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critic...
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553
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GATE Mechanical 2021 Set 1 | Question: 5
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with...
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GATE Mechanical 2021 Set 1 | Question: 33
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes ...
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614
614 views
GATE2020-ME-2: 36
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in the next ...
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521
521 views
GATE2020-ME-2: 1
The sum of two normally distributed random variables $X$ and $Y$ isalways normally distributednormally distributed, only if $X$ and $Y$ are independentnormally distribute...
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755
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GATE Mechanical 2014 Set 1 | Question: 28
In the following table, $x$ is a discrete random variable and $p(x)$ is the probability density. The standard deviation of $x$ is$$\begin{array}{|c|c|c|c|} \hline x & 1 &...
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GATE2019 ME-2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
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459
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GATE2019 ME-2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at le...
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729
729 views
GATE2019 ME-1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability di...
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956
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GATE2018-2-24
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between s...
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1.4k
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GATE2018-2-27
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ isexponentially...
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397
397 views
GATE2018-1-26
Let $X_1, \: X_2$ be two independent normal random variables with means $\mu_1, \: \ \mu_2$ and standard deviations $\sigma_1, \: \sigma_2$, respectively. Consider $Y=X_1...
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315
315 views
GATE2018-1-1
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probabil...
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333
333 views
GATE2017 ME-2: 24
The standard deviation of linear dimensions $P$ and $Q$ are $3 \mu$ m and $4 \mu$ m, respectively. When assembled, the standard deviation (in $\mu$ m) of the resulting li...
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291
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GATE2017 ME-2: 4
A sample of $15$ data is as follows: $17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3$. The mode of the data is$4$$13$$17$$20$
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309
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GATE2017 ME-2: 1
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.
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308
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GATE2017 ME-1: 5
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.
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375
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GATE2016-3-29
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is$\dfrac{16}{5525} \\$$\dfrac{64}{2197} \\$$\dfrac{3}{13} \\$...
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362
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GATE2016-3-4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
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301
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GATE2016-2-28
The probability that a screw manufactured by a company is defective is $0.1$. The company sells screws in packets containing $5$ screws and gives a guarantee of replaceme...
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