# Probability and Statistics · Engineering Mathematics · GATE CE

Start Practice## Marks 1

GATE CE 2024 Set 1

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. ...

GATE CE 2023 Set 2

Which of the following probability distribution functions (PDFs) has the mean greater than the median?
...

GATE CE 2023 Set 2

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without polluti...

GATE CE 2023 Set 1

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A ...

GATE CE 2017 Set 2

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...

GATE CE 2017 Set 1

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

GATE CE 2016 Set 2

The spot speeds (expressed in km/hr) observed at a road section are $$66, 62, 45, 79, 32, 51, 56, 60, 53$$ and $$49.$$ The median speed (expressed in ...

GATE CE 2016 Set 2

$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right) = 0.7.$$ Which one of the fol...

GATE CE 2016 Set 1

Type $${\rm I}{\rm I}$$ error in hypothesis testing is

GATE CE 2014 Set 2

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 pro...

GATE CE 2012

The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200$$ mm, respectively. The proba...

GATE CE 2010

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing

GATE CE 2008

Three values of $$x$$ and $$y$$ are to be fitted in a straight line in the form $$y=a+bx$$ by the method of least squares. Given $$\,\,\,\sum x = 6,\...

GATE CE 2007

If the standard deviation of the speed of vehicles in a highway is $$8.8$$ kmph and the mean speed of the vehicles is $$33$$ kmph, the coefficient of...

GATE CE 2003

A box contains $$10$$ screws, $$3$$ of which are defective. Two screws are drawn at random with replacement. The probability that none of the two scre...

## Marks 2

GATE CE 2024 Set 2

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X red...

GATE CE 2024 Set 1

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the proba...

GATE CE 2022 Set 2

A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _...

GATE CE 2017 Set 1

For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements...

GATE CE 2016 Set 2

If $$f(x)$$ and $$g(x)$$ are two probability density functions,
$$$f\left( x \right) = \left\{ {\matrix{
{{x \over a} + 1} & : & { - a \le...

GATE CE 2015 Set 2

The probability density function of a random variable, $$x$$ is
$$$\matrix{
{f\left( x \right) = {x \over 4}\left( {4 - {x^2}} \right)} & {for...

GATE CE 2015 Set 2

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?

GATE CE 2015 Set 1

Consider the following probability mass function (p.m.f) of a random variable $$X.$$
$$$p\left( {x,q} \right) = \left\{ {\matrix{
q & {if\,X =...

GATE CE 2014 Set 1

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by
$$$f\left( E \right) = \left\{ {\matrix{
...

GATE CE 2014 Set 1

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...

GATE CE 2014 Set 2

An observer counts $$240$$veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probabilit...

GATE CE 2014 Set 2

If $$\left\{ x \right\}$$ is a continuous, real valued random variable defined over the interval $$\left( { - \infty ,\,\, \pm \infty } \right)$$ and ...

GATE CE 2013

Find the value of $$\lambda $$ such that the function $$f(x)$$ is a valid probability density function ________.

GATE CE 2012

Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

GATE CE 2011

There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball...

GATE CE 2009

The standard normal probability function can be approximated as
$$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}...

GATE CE 2004

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed...