GATE ME

Probability and Statistics

Engineering Mathematics

(Past Years Questions)

Marks 1

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Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ...
GATE ME 2017 Set 2
A simple 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
GATE ME 2017 Set 2
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________.
GATE ME 2017 Set 1
The area (in percentage) under standard normal distribution curve of variable $$Z$$ within limits from $$-3$$ to $$+3$$ ...
GATE ME 2016 Set 3
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu $$. The standa...
GATE ME 2016 Set 1
If $$P(X)$$ $$ = $$ $$1/4,$$ $$P(Y) = 1/3,$$ and $$\,\,P\left( {X \cap Y} \right) = 1/12,\,\,$$ the value of $$P(Y/X)$$...
GATE ME 2015 Set 3
The probability of obtaining at least two $$'SIX'$$ in throwing a fair dice $$4$$ times is
GATE ME 2015 Set 1
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is ...
GATE ME 2015 Set 1
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance...
GATE ME 2015 Set 1
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution wit...
GATE ME 2014 Set 4
The number of accidents occurring in a plant in a month follows Poisson distribution with mean as $$5.2.$$ The probabil...
GATE ME 2014 Set 4
A group consists of equal number of men and women. Of this group $$20$$% of the men and $$50$$% of the women are unemplo...
GATE ME 2014 Set 3
Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X ...
GATE ME 2013
A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without ...
GATE ME 2010
If three coins are tossed simultaneously, the probability of getting at least one head is
GATE ME 2009
The standard deviation of a uniformly distributed random variable $$b/w$$ $$0$$ and $$1$$ is
GATE ME 2009
A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?
GATE ME 2008
A lot had $$10$$% defective items. Ten items are chosen randomly from this lot. The probability that exactly $$2$$ of th...
GATE ME 2005
Using given data points tabulated below, a straight line passing through the origin is fitted using least squares method...
GATE ME 2005
A regression model is used to express a variable $$Y$$ as a function of another variable $$X.$$ This implies that
GATE ME 2002
The probability that two friends share the same birth-month is
GATE ME 1998

Marks 2

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Three cards were drawn from a pack of $$52$$ cards. The probability that they are a king, a queen, and a jack is
GATE ME 2016 Set 3
The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets con...
GATE ME 2016 Set 2
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event...
GATE ME 2015 Set 3
The chance of a student passing an exam is $$20$$% The chance of a student passing the exam and getting above $$90$$% ma...
GATE ME 2015 Set 2
A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3}$...
GATE ME 2014 Set 3
A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner f...
GATE ME 2014 Set 2
Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such t...
GATE ME 2014 Set 2
In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard devia...
GATE ME 2014 Set 1
The probability that a student knows the correct answer to a multiple choice question is $${2 \over 3}$$. If the studen...
GATE ME 2013
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, ...
GATE ME 2012
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $...
GATE ME 2012
An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at le...
GATE ME 2011
Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ varianc...
GATE ME 2007
A single die is thrown two times. What is the probability that the sum is neither $$8$$ nor $$9?$$
GATE ME 2005
From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kin...
GATE ME 2004
The following data about the flow of liquid was observed in a continuous chemical process plant Mean flow rate of th...
GATE ME 2004
In a manufacturing plant, the probability of making a defective bolts is $$0.1$$. The mean and standard deviation of def...
GATE ME 2000
Four arbitrary points $$\,\,\,\left( {{x_1},{y_1}} \right),\,\,\left( {{x_2},{y_2}} \right),\,\,\left( {{x_3},{y_3}} \ri...
GATE ME 1999

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