GATE ME
Engineering Mathematics
Probability and Statistics
Previous Years Questions

## Marks 1

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _________.
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
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________.
The area (in percentage) under standard normal distribution curve of variable $$Z$$ within limits from $$-3$$ to $$+3$$ is ________.
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu$$. The standard deviation for this distribu...
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
The probability of obtaining at least two $$'SIX'$$ in throwing a fair dice $$4$$ times is
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 ...
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? ...
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...
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 ...
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...
Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}$$ is
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 ...
If three coins are tossed simultaneously, the probability of getting at least one head is
The standard deviation of a uniformly distributed random variable $$b/w$$ $$0$$ and $$1$$ is
A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?
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...
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 ...
A regression model is used to express a variable $$Y$$ as a function of another variable $$X.$$ This implies that
The probability that two friends share the same birth-month is

## Marks 2

Three cards were drawn from a pack of $$52$$ cards. The probability that they are a king, a queen, and a jack is
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...
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...
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...
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...
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...
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...
In the following table, $$x$$ is a discrete random variable and $$p(x)$$ is the probability density. The standard deviation of $$x$$ is ...
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...
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...
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the s...
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 _______.
Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ variance $$\left( {{V_{ar}}} \right)... A single die is thrown two times. What is the probability that the sum is neither$$8$$nor$$9?$$From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kings, if the card is NOT replace... The following data about the flow of liquid was observed in a continuous chemical process plant Mean flow rate of the liquid is ... In a manufacturing plant, the probability of making a defective bolts is$$0.1$$. The mean and standard deviation of defective bolts in a total of$$9...
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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