probability

A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administrati...

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,...

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 compa...

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

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

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 mo...

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 c...

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...

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a...

Let X be a continuous random variable defined on [0,1] such that its probability density function f(x) = 1 for 0 ≤ x ≤ 1 and 0 otherwise. Let Y = loge(X + 1). Then the expected val...

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...

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...

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...

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).

The mean and variance, respectively, of a binomial distribution for n independent trials with the probability of success as p, are

A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and...

Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop...

Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity...

The lengths of a large stock of titanium rods follow a normal distribution with a mean ($\mu$) of 440 mm and a standard deviation ($\sigma$) of 1 mm. What is the percentage of rods...

The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probab...

The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts...

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is

Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that a...

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

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, th...

A six-faced fair dice is rolled five times. The probability (in %) of obtaining "ONE" at least four times is

The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive cu...

Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is

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, th...

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _________.

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

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

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 examina...

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 $$1/8$$. What is the probabili...

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...

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...

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 d...

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...

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...

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

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 answ...

Let $$X$$ be a normal random variable with mean $$1$$ and variance $$4.$$ The probability $$P\left\{ {X < 0} \right\}$$ is

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 absorb...

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 c...

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 f...

The standard deviation of a uniformly distributed random variable $$b/w$$ $$0$$ and $$1$$ is

If three coins are tossed simultaneously, the probability of getting at least one head is

A coin is tossed $$4$$ times. What is the probability of getting heads exactly $$3$$ times?

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

At a production machine, parts arrive according to a Poisson process at the rate of $$0.35$$ parts per minute. Processing time for parts have exponential distribution with mean of...

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