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GATE CSE

Probability

Discrete Mathematics

Previous Years Questions

Marks 1

More
Two numbers are chosen independently and uniformly at random from the set {1, 2, ...., 13}. The probability (rounded off...
GATE CSE 2019
Let $$X$$ be a Gaussian random variable with mean $$0$$ and variance $${\sigma ^2}$$ . Let $$Y=max(X,0)$$ where $$max(a,...
GATE CSE 2017 Set 1
A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interva...
GATE CSE 2016 Set 1
The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the ...
GATE CSE 2014 Set 2
Each of the nine words in the sentence "The Quick brown fox jumps over the lazy dog" is written on a separate piece of p...
GATE CSE 2014 Set 2
Suppose you break a stick of unit length at a point chosen uniformaly at random. Then the expected length of the shorter...
GATE CSE 2014 Set 1
Suppose p is the number of cars per minute passing through a certain road junction between 5PM and 6PM and p has a poiss...
GATE CSE 2013
Consider a random variable X that takes values + 1 and-1 with probability 0.5 each. The values of the cumulative distr...
GATE CSE 2012
If the difference between the expectation of the square of a random variable $$\left( {E\left[ {{X^2}} \right]} \right)$...
GATE CSE 2011
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both ...
GATE CSE 2011
A sample space has two events A and B such that probabilities $$P\,(A\, \cap \,B)\, = \,1/2,\,\,P(\overline A )\, = \,1...
GATE CSE 2008
Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives he...
GATE CSE 2007
In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data ...
GATE CSE 2006
Let $$f(x)$$ be the continuous probability density function of a random variable X. The probability that $$a\, < \,X\...
GATE CSE 2005
A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded...
GATE CSE 2005
If a fair coin is tossed four times, what is the probability that two heads and two tails will result?
GATE CSE 2004
In a population of N families, 50% of the families have three children, 30% of the families have two children and the re...
GATE CSE 2004
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em...
GATE CSE 2003
Suppose that the expectation of a random variable X is 5. Which of the following statements is true?
GATE CSE 1999
Suppose that the expectation of a random variable X is 5. Which of the following statements is true?
GATE CSE 1999
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is
GATE CSE 1998
The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that ...
GATE CSE 1997
Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is
GATE CSE 1996
The probability that a number selected at random between $$100$$ and $$999$$ (both inclusive ) will not contain the digi...
GATE CSE 1995
Let A and B be any two arbitrary events, then, which one of the following is true?
GATE CSE 1994

Marks 2

More
A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively,...
GATE CSE 2021 Set 1
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially d...
GATE CSE 2021 Set 1
Consider the two statements. S1 : There exist random variables X and Y such that (E[X - E(X)) (Y - E(Y))])2 > ...
GATE CSE 2021 Set 1
For n > 2, let a {0, 1}n be a non-zero vector. Suppose that x is chosen uniformly at random from {0, 1}n. Then, the p...
GATE CSE 2020
Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 ha...
GATE CSE 2019
Consider Guwahati $$(G)$$ and Delhi $$(D)$$ whose temperatures can be classified as high $$(H),$$ medium $$(M)$$ and low...
GATE CSE 2018
Two people, $$P$$ and $$Q,$$ decide to independently roll two identical dice, each with $$6$$ faces, numbered $$1$$ to $...
GATE CSE 2018
For any discrete random variable $$X,$$ with probability mass function $$P\left( {X = j} \right) = {p_j},$$ $${p_j}\,\, ...
GATE CSE 2017 Set 2
If a random variable $$X$$ has a Poisson distribution with mean $$5,$$ then the expectation $$E\left[ {{{\left( {X + 2} ...
GATE CSE 2017 Set 2
$$P$$ and $$Q$$ are considering to apply for a job. The probability that $$P$$ applies for the job is $${1 \over 4},$$ t...
GATE CSE 2017 Set 2
Consider the following experiment. Step1: Flip a fair coin twice. Step2: If the outcomes are (TAILS, HEADS) then output...
GATE CSE 2016 Set 1
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more...
GATE CSE 2016 Set 2
Suppose $${X_i}$$ for $$i=1,2,3$$ are independent and identically distributed random variables whose probability mass fu...
GATE CSE 2015 Set 3
The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c$$ respectively. Of th...
GATE CSE 2015 Set 1
Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$ ...
GATE CSE 2015 Set 1
Let S be a sample space and two mutually exclusive events A and B be such that $$A\, \cup \,B = \,S$$. If P(.) denotes t...
GATE CSE 2014 Set 3
The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ...
GATE CSE 2014 Set 2
Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is__...
GATE CSE 2014 Set 1
Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2 or 3 the die is rolled a second time. What ...
GATE CSE 2012
Consider a finite sequence of random values $$X = \left\{ {{x_1},{x_2},{x_3}, - - - - - {x_n}} \right\}..$$ Let $${\...
GATE CSE 2011
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one ...
GATE CSE 2011
Consider a company that assembles computers. The probability of a faulty assembly of any computer is P. The company ther...
GATE CSE 2010
What is the probability that divisor of $${10^{99}}$$ is a multiple of $${10^{96}}$$ ?
GATE CSE 2010
An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of ...
GATE CSE 2009
What is the probability that in a randomly choosen group of r people at least three people have the same birthday?
GATE CSE 2008
Let X be a random variable following normal distribution with mean + 1 and variance 4. Let Y be another normal variable ...
GATE CSE 2008
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the pr...
GATE CSE 2008
Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3,..., 20. What is the promuta...
GATE CSE 2007
When a coin is tossed, the probability of getting a Head is p, 0 < p < 1. Let N be the random variable denoting th...
GATE CSE 2006
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on o...
GATE CSE 2005
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the tails ar...
GATE CSE 2005
Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows: (i) sel...
GATE CSE 2005
Two n bit binary stings, S1 and, are chosen randomly with uniform probability. The probability that the Hamming distance...
GATE CSE 2004
An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each in...
GATE CSE 2004
A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at (0, 0), (1...
GATE CSE 2004
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is
GATE CSE 2002
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?
GATE CSE 2001
$${{E_1}}$$ and $${{E_2}}$$ are events in a probability space satisfying the following constraints: $$ \bullet $$ $$\Pr...
GATE CSE 2000
Consider two events $${{E_1}}$$ and $${{E_2}}$$ such that probability of $${{E_1}}$$, Pr [$${{E_1}}$$] = 1/2, probabilit...
GATE CSE 1999
Let X and Y be two exponentially distributed and independent random variables with mean $$\alpha $$ and $$\beta $$, resp...
GATE CSE 1999
The probability that the top and bottom cards of a randomly shuffled deck are both access is
GATE CSE 1996
A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is bla...
GATE CSE 1995

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