Probability & Stats (ME)

If two unbiased coins are tossed, then what is the probability of having at least one head?

A final year student appears for placement interview in two companies, $S$ and $T$. Based on her interview performance, she estimates the probability of receiving job offers from companies $S$ and $T$ to be 0.8 and 0.6 ,...

P and Q play chess frequently against each other. Of these matches, P has won $80 \%$ of the matches, drawn $15 \%$ of the matches and lost $5 \%$ of the matches. If they play 3 more matches, what is the probability of $...

Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the fo...

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

Let $X$ be a continuous random variable defined on $[0, 1]$ such that its probability density function $f(x) = 1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y = \log_e (X + 1)$. Then the expected value of $Y$ is _____...

A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the...

How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?

Let a random variable X follow Poisson distribution such that Prob(X = 1) = Prob(X = 2). The value of Prob(X = 3) is __________ (round off to 2 decimal places).

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from th...

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________.

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

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $$\mu $$. The standard deviation for this distribution is given by

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 guarantee of replacement if one or more screws in the packet are fou...

Three cards were drawn from a pack of $$52$$ cards. The probability that they are a king, a queen, and a jack is

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 that a student passes the examination, the probability that the student g...

The probability of obtaining at least two $$'SIX'$$ in throwing a fair dice $$4$$ times is

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

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 $$1/8$$. What is the probability that only one of them will be selecte...

Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such that each color appears only two times on the die. If the die is thrown thrice, the probability of ob...

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 standard deviation of Rs. $$50.$$ The percentage of savings account ho...

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 of both the parts being good is

A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3}$$ and $${1 \over 6}$$, respectively. Then mean value and the variance of the number of defective pie...

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 at random from this group, the probability of the selected person being...

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 $$2$$ accidents in the plant during a randomly selected month is _____...

Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}$$ 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, then the student guesses the answer. The probability of the guessed answe...

A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls...

An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the shock absorbers. All shock absorbers are subjected to a quality test. The...

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 _______.

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 of drawing $$2$$ washers first followed by $$3$$ nuts and subsequently t...

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?

Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ variance $$\left( {{V_{ar}}} \right)$$ and covariance $$\left( {{C_{ov}}} \right)$$ given below is FALSE?

A single die is thrown two times. What is the probability that the sum is neither $$8$$ nor $$9?$$

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 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 $$900$$ bolts are respectively

Four arbitrary points $$\,\,\,\left( {{x_1},{y_1}} \right),\,\,\left( {{x_2},{y_2}} \right),\,\,\left( {{x_3},{y_3}} \right),\,\,\left( {{x_4},{y_4}} \right),\,\,\,\,$$ are given in the $$xy$$ $$-$$ plane using the metho...

The probability that two friends share the same birth-month is