# Probability and Statistics · Engineering Mathematics · GATE ME

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## Marks 1

GATE ME 2017 Set 2
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 1
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________.
GATE ME 2016 Set 3
The area (in percentage) under standard normal distribution curve of variable $$Z$$ within limits from $$-3$$ to $$+3$$ is ________.
GATE ME 2016 Set 1
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu$$. The standard deviation for this distribu...
GATE ME 2015 Set 3
If $$P(X)$$ $$=$$ $$1/4,$$ $$P(Y) = 1/3,$$ and $$\,\,P\left( {X \cap Y} \right) = 1/12,\,\,$$ the value of $$P(Y/X)$$ is
GATE ME 2015 Set 1
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 $$1/6$$ and that of Ramesh 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 2014 Set 4
The number of accidents occurring in a plant in a month follows Poisson distribution with mean as $$5.2.$$ The probability of occurrence of less than...
GATE ME 2014 Set 4
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. $$500$$ and a ...
GATE ME 2014 Set 3
A group consists of equal number of men and women. Of this group $$20$$% of the men and $$50$$% of the women are unemployed. If a person is selected a...
GATE ME 2013
Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}$$ is
GATE ME 2010
A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without replacement. The probability ...
GATE ME 2009
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 2008
A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?
GATE ME 2005
A lot had $$10$$% defective items. Ten items are chosen randomly from this lot. The probability that exactly $$2$$ of the chosen items are defective i...
GATE ME 2005
Using given data points tabulated below, a straight line passing through the origin is fitted using least squares method. The slope of the line is ...
GATE ME 2002
A regression model is used to express a variable $$Y$$ as a function of another variable $$X.$$ This implies that
GATE ME 1998
The probability that two friends share the same birth-month is

## Marks 2

GATE ME 2016 Set 3
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 2
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...
GATE ME 2015 Set 3
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 that a tail occurs on the thi...
GATE ME 2015 Set 2
The chance of a student passing an exam is $$20$$% The chance of a student passing the exam and getting above $$90$$% marks in it is $$5$$%. Given tha...
GATE ME 2014 Set 2
A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability o...
GATE ME 2014 Set 2
Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such that each color appears only tw...
GATE ME 2014 Set 3
A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3}$$ and $${1 \over 6}$$, respect...
GATE ME 2014 Set 1
In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard deviation of $$x$$ is ...
GATE ME 2013
The probability that a student knows the correct answer to a multiple choice question is $${2 \over 3}$$. If the student does not know the answer, th...
GATE ME 2012
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The proba...
GATE ME 2012
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the s...
GATE ME 2011
An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at least one head is _______.
GATE ME 2007
Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ variance $$\left( {{V_{ar}}} \right)... GATE ME 2005 A single die is thrown two times. What is the probability that the sum is neither$$8$$nor$$9?$$GATE ME 2004 From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kings, if the card is NOT replace... GATE ME 2004 The following data about the flow of liquid was observed in a continuous chemical process plant Mean flow rate of the liquid is ... GATE ME 2000 In a manufacturing plant, the probability of making a defective bolts is$$0.1$$. The mean and standard deviation of defective bolts in a total of$$9...
GATE ME 1999
Four arbitrary points \,\,\,\left( {{x_1},{y_1}} \right),\,\,\left( {{x_2},{y_2}} \right),\,\,\left( {{x_3},{y_3}} \right),\,\,\left( {{x_4},{y_4}} ...
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