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Recent questions tagged probability

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GATE Civil 2024 Set 1 | Question: 3
​​​​​​The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probabilit...
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GATE Civil 2024 Set 1 | Question: 5
Concrete of characteristic strength $30 \mathrm{MPa}$ is required. If $40$ specimens of concrete cubes are to be tested, the minimum number of specimens having at least $...
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GATE Civil 2021 Set 2 | GA | Question: 3
Two identical cube shaped dice each with faces numbered $1$ to $6$ are rolled simultaneously. The probability that an even number is rolled out on each dice is:$\frac{1}{...
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GATE2020-CE-1-18
The probability that a $50$ year flood may $\textbf{NOT}$ occur at all during $25$ years life of a project (round off to two decimal places), is _______.
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GATE2020 CE-2-18
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
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GATE2017 CE-2-20
A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the c...
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GATE Civil 2017 Set 2 | GA | Question: 5
Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is$\dfrac{1}{9} \\$$\dfrac{...
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GATE2019 CE-1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flo...
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GATE2019 CE-2: 26
The probability density function of a continuous random variable distributed uniformly between $x$ and $y$ (for $y>x$) is$\dfrac{1}{x-y}$$\dfrac{1}{y-x}$$x-y$$y-x$
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GATE2016-2-4
$X$ and $Y$ are two random independent events. It is known that $P(X)=0.40$ and $P(X \cup Y^C)=0.7$. Which one of the following is the value of $P(X \cup Y)$?$0.7$$0.5$$0...
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GATE2016-2-27
If $f(x)$ and $g(x)$ are two probability density functions,$f(x) = \begin{cases} \dfrac{x}{a}+1 & :-a \leq x < 0 \\ -\dfrac{x}{a}+1 & : 0 \leq x \leq a \\ 0 & :\text{oth...
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GATE2016-1-26
Probability density function of a random variable $X$ is given below$$f(x) = \begin{cases} 0.25 & \text{ if } 1 \leq x \leq 5 \\ 0 & \text{ otherwise} \end{cases}$$$P(X \...
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GATE2017 CE-1: 2
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are$2$ and $2$$1$ and $2$$2$ and $1$$1$ and $1$
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GATE2017 CE-1: 26
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct?$a=1,b=4$$b=0.5,b=1$$a=0,b=1$$a=1,b...
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1 answers 1 answer
GATE Civil 2015 Set 2 | GA | Question: 5
Four cards are randomly selected from a pack of $52$ cards. If the first two cards are kings, what is the probability that the third card is a king?$\dfrac{4}{52} \\$$\df...
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GATE2015-2-26
The probability density function of a random variable, $x$ is$f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{ca...
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GATE2015-1-3
Consider the following probability mass function (p.m.f) of a random variable $X:$$$p(x,q) = \begin{cases} q & \text{ if } X=0 \\ 1 – q & \text{ if } X=1 \\ 0 & \text{oth...
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GATE Civil 2014 Set 2 | GA | Question: 10
$10\%$ of the population in a town is $HIV^{+}$. A new diagnostic kit for HIV detection is available, this kit correctly identifies $HIV^{+}$ individuals $95\%$ of the ti...
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GATE Civil 2014 Set 2 | GA | Question: 4
In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04.$ The average time between successive occurrenc...
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GATE2014-2-27
An observer counts $240$ veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probability of having one havin...
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GATE2014-2-5
If $\{x\}$ is a continuous, real valued random variable defined over the interval $(- \infty, + \infty)$ and its occurrence is defined by the density function given as: $...
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GATE2014-2-1
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtainin...
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GATE2014-1-29
A traffic office imposes on an average $5$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follow...
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GATE2014-1-3
The probability density function of evaporation $E$ on any day during a year in a watershed is given by$f(E) = \begin{cases} \dfrac{1}{5} & 0 \leq E \leq 5\: \text{mm/day...
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GATE Civil 2013 | Question: 29
Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______$f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \...
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GATE Civil 2013 | Question: 3
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in eac...
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GATE Civil 2012 | Question: 65
An automobile plant contracted to buy shock absorbers from two suppliers $X$ and $Y.$ $X$ supplies $60\%$ and $Y$ supplies $40\%$ of the shock absorbers. All shock absorb...
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GATE Civil 2012 | Question: 27
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is$\dfrac{1}{32} \\$$\d...
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GATE Civil 2012 | Question: 2
The annual precipitation data of a city is normally distributed with mean and standard deviation as $1000$ mm and $200$ mm, respectively. The probability that the annual ...
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GATE2018 CE-2: 19
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
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GATE2018 CE-2: 2
The graph of a function $f(x)$ is shown in the figure.For $f(x)$ to be a valid probability density function, the value of $h$ is$1/3$$2/3$$1$$3$
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