ISI MS QE Mock Test

What is the probability of 53 Sundays in a leap year

Tickets numbered 1 to 200 are mixed and a ticket is drawn at random from them. What is the probability that the ticket drawn is a multiple of 3

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

What is the Probability of getting a sum 9 from two throws of a dice

Two dice are rolled simultaneously. The probability that total score is prime number is

Let A and B be two mutually exclusive events with positive probability each, defined on the same sample space. Find the correct answer:

An unbiased coin is tossed until a head appears. The expected number of tosses required is

A card is drawn at random from an ordinary deck of cards. If an ace is drawn you win Rs. 100; if a king is drawn you win Rs. 75; if a queen is drawn you win Rs. 50; and if a jack is drawn you win Rs. 25. What is the probability of winning at least Rs. 25? What would you expect to win on average?

Among 25 articles, 9 are defective, 6 have only minor defects and 3 have major defects. The probability that, if a selected article is defective, then the defect is major is

A student must choose one of the subjects - Physics, Chemistry or Mathematics for study. She is equally likely to choose Physics or Chemistry and twice as likely to choose Mathematics. The probability that student chooses Mathematics is

If A and B are independent events, P(A) = 0.5, P(A U B) = 0.7, then P(B) is

A car with six spark plugs is known to have two defective spark plugs. If two plugs are pulled at random, then the probability that both are defective is :

If E(XY) = 36, E(X) = 9, E(Y) = 4 then

Events A and B are equally likely and are independent. The probability of the event A and B is 0.36. The probability of A is :

If P(A) = P(B) = p, then P[A ∩ B] 

Given P(A) = 0.5, P(B) = 0.4 if A and B are independent then P(A U B) is

If a fair coin is tossed twice, the probability of getting 'head' at least once is 

If two fair dice are tossed, the probability that the sum of the points on the dice equals 7 is 

If A and B are independent events then

Given P(A) = 0.4, P(A U B) = 0.7, and A and B are independent, P(B) is equal to

Consider an examinee answering a multiple-choice examination. For a particular question with 4 choices, the probability that the examinee knows the answer is 1/3, the probability that she makes the correct choice given that she knows the answer is 1, and the probability that she makes the correct choice given that she does not know the answer is ¼. The probability that she knew the answer given that she has made the correct choice is

A random variable has outcomes Success and Failure with probabilities 3/4 and 1/4 respectively. A gambler observes the sequence of outcomes of this variable and receives a prize of 2ⁿ if n is the first time that success occurs. what is the expected value of the gambler's prize?

A box contains 10 fuses, 4 of which are defective. If 3 of the fuses are drawn without replacement, what is the probability that all three are defective?

Suppose two dice are tossed simultaneously. What is the probability that the total number of spots on the upper faces of the two dice is not divisible by 2, 3 or 5?

There are three women on the platform of a train station. The train that they are waiting for has 5 coaches and each of them is equally likely to enter any coach. What is the probability that they will all enter the same coach?

There are three identical boxes, each with two drawers. Box A contains a gold coin in each drawer. Box B contains a silver coin in each drawer. Box C contains a gold coin in one drawer and a silver coin in another drawer. A box is chosen at random, a drawer opened and a gold coin is found. What is the probability that the chosen box is A?

If a point is taken at random from within a circle with radius r, what is the probability that its distance from the center will exceed r/2?

Each of the four economists is asked to prescribe one out of four economic policies. Each economist is equally likely to prescribe any of the four different policies. what is the probability that each of the economists prescribes a different policy?

Consider the experiment of tossing two unbiased coin in succession. What is the probability of obtaining two heads, given that at least one of the coins comes up heads?

A lot consists of 10 articles, 4 with minor defects and 2 with major defects. If 2 articles are picked at random, the probability that both have minor defects is

Suppose a neighborhood has 90 Hindus and 10 Muslims. What is the probability that two randomly selected persons from that neighborhood will have the same religion?

A dog has two puppies and a cat has two kittens. You know the older puppy is male. You also know that at least one of the kittens is male. what are the probabilities that the dog and the cat each have two male offsprings?

A blood test to detect the presence of a certain disease detects the disease in 99 out of every 100 patients who actually have the disease. But it falsely indicates the presence of the disease in 1 out of every 100 healthy persons. 1 percent of the population has the disease. The test is administered to a randomly selected person. What is the probability that she has the disease given that her result is positive?

If one integer is chosen at random from the sequence 1, ..., 50, the probability that the chosen number is divisible by 6 or 8 is 

The depositors at save more bank are categorized by age and sex. We are going to select an individual at random from this group of 2000 depositors.

Age                    Male        Female

30 or Less       800          600

31 or More      400          200

Then probability the depositor is Female =

The depositors at save more bank are categorized by age and sex. We are going to select an individual at random from this group of 2000 depositors.

Age                    Male        Female

30 or Less       800          600

31 or More      400          200

What is the conditional probability that the depositor is 30 or less given that he is male?

Suppose four coins are tossed simultaneously. Suppose E is the event “the number of heads strictly exceeds the number of tails” and F is the event “the number of Tails strictly exceeds the number of Heads” what is the probability of the event  E U F?

Three distinct points X, Y and Z are taken at random on a line segment. What is the probability that Z lies between X and Y?

A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face (for example a six is three times as probable as two). what is the probability of getting an even number in one throw?

ICICI bank collects data on 10000 respondents. Out of the 6800 men, 4200 have credit cards, and out of the 3200 women, 2500 have credit cards. Out of the men with credit cards, 1200 have unpaid balances, whereas out of the women with credit cards, 1400 have unpaid balances. What is the probability that an individual selected at random is a man without an unpaid balance?

Amit has box containing 6 red balls and 3 green balls. Amita has a box containing 4 red balls and 5 green balls. Amit randomly draws one ball from his box and puts it into Amita’s box. Now Amita randomly draws one ball out of her box. What is the probability that the balls drawn by Amit and Amita were of different colours?

A survey of asset ownership in poor households in rural UP and Bihar found that 40% of the households own a radio, 15% own a television and 60% own a bicycle. It also found that 5% of the households own both a radio and a television, 26% own both a radio and a bicycle, 5% own both a television and a bicycle, and 1% own all three. If a randomly selected poor household in these areas is found to own exactly one of these three assets, what is the probability that it is a bicycle?

A primary school has 6 classes, numbered from 1 to 6. Class 1 has twice as many students as each of the other classes. What is the probability that a randomly selected student is from an odd numbered class?

A blood test detects a given disease with probability 8/10 given that the tested person actually has the disease. With probability 2/10, the test incorrectly shows the presence of the disease in a disease free person. Suppose 1/10 of the population has the disease. What is the probability that the person tested actually has the disease if the test indicates the presence of the disease?

Three players A, B and C take turns playing a game as follows :

A and B play in the first round. The winner plays C in the second round, while the loser sits out. The winner of the second round plays the person who was sitting out. The game continues in this fashion, with the winner of the current round playing the next round with the person who sits out in the current round. The game ends when a player wins twice in succession; this player is declared the winner of the contest. For any of the rounds, assume that the two players playing the round each have a probability of 1/2 of winning the round, regardless how the past rounds were won or lost.

The probability that A becomes the winner of the contest is 

Let A and B be any two events, each of which has a positive probability of occurring. Consider the following statements

          I        If A and B are independent, they must be mutually exclusive

          II       If A and B are mutually exclusive, they must be independent

          III      If A and B are independent, they cannot be mutually exclusive

          IV      If A and B are mutually exclusive, they cannot be independent

          Which of the above statements are true?

There are three identical boxes, each with two drawers. Box A contains a gold coin in each drawer. Box B contains a silver coin in each drawer. Box C contains a gold coin in one drawer and a silver coin in another drawer. A box is chosen at random, a drawer opened and a gold coin is found. What is the probability that the chosen box is A?

There are 3 red and 5 black balls in an urn. You draw two balls in succession without replacing the first ball. What is the probability that the second ball you draw is red?

Suppose that 80% of all statisticians are shy, whereas only 15% of all economists are shy. Suppose also that 90% of the people at a large gathering are economists and the other 10% are statisticians. If you meet a shy person at random at the gathering, what is the probability that the person is a statistician?

Three players A, B and C take turns playing a game as follows :

A and B play in the first round. The winner plays C in the second round, while the loser sits out. The winner of the second round plays the person who was sitting out. The game continues in this fashion, with the winner of the current round playing the next round with the person who sits out in the current round. The game ends when a player wins twice in succession; this player is declared the winner of the contest. For any of the rounds, assume that the two players playing the round each have a probability of 1/2 of winning the round, regardless how the past rounds were won or lost.

The probability that the game continues indefinitely with no one winning twice in succession, is

Your teacher knows 6 jokes and in each class tells 2 jokes, each joke has an equal chance of being selected. What is the probability that, in a given lecture, at least 1 joke is told that was not told in the previous class?

Consider an experiment in which five fibers having different lengths are subjecting to a testing process to learn which fiber will break first. The lengths of the five fibers 1 inch, 2 inches, 3 inches, 4 inches and 5 inches. Suppose the probability that any fiber will be the first to break is proportional to the length of that fiber. The probability that the length of the fiber that breaks first is not more than 3 inches is :

Three players A, B and C take turns playing a game as follows :

A and B play in the first round. The winner plays C in the second round, while the loser sits out. The winner of the second round plays the person who was sitting out. The game continues in this fashion, with the winner of the current round playing the next round with the person who sits out in the current round. The game ends when a player wins twice in succession; this player is declared the winner of the contest. For any of the rounds, assume that the two players playing the round each have a probability of 1/2 of winning the round, regardless how the past rounds were won or lost.

The probability that C becomes the winner of the contest is 

The average travel time to a distant city is w hours by train or z hours by bus. A man cannot decide whether to take the train or the bus, so he chooses a coin. What is his expected travel time?

Two patients share a hospital room for two days. Suppose that, on any given day, a person independently picks up an airborne infection with probability 1/4. An individual who is infected on the first day will certainly pass it to the other patient on the second day. Once contracted, the infection stays for at least two days. What is the probability that both patients have contracted the infection by the end of the second day?

A class has 6 students, randomly divided into two teams, A and B, for a race. What is the probability that the three runners in team A will come in first, second and third?

Suppose that each person out of a group of 4 persons is randomly assigned to one of 6 classes. What is the probability that no class has more than one person from this group?

A fair dice has numbers 1,2,3, 4, 5 and 6 on its sides. It is tossed once. I win Rs. 1 if an odd number shows up; otherwise I lose Rs.1. Let X be the number that shows up and Y the money I win.

[Note: Y < 0 if I lose money.] Which of the following is incorrect? 

The nine digits 1, 2,…, 9 are arranged in random order to form a nine digit number, which uses each digit exactly once. Find the probability that 1, 2 and 3 appear as neighbours in the increasing order. 

A traffic light on the way to the university is red 40% of the time. What’s the probability of getting a red light (i) 2 days in a row, (ii) any 2 out of 3 days.

Consider two events A and B with Pr(A) = 0.4 and Pr(B) = 0.7 The maximum and minimum values of Pr(A∩B) respectively are:

Let A1, A2, A3 be independent events with probabilities p1, p2, p3 respectively. The probability that none of these event occur equals

Suppose, you are an editor of a magazine. Everyday you get two letters from your correspondents. Each letter is as likely to be from a male as from a female correspondent. The letters are delivered by a postman, who brings one letter at a time. Moreover, he has a ‘ladies first’ policy; he delivers letter from a female first, if there is such a letter. Suppose you have already received the first letter for today and it is from a female correspondent. What is the probability that the second letter will also be from a female? 

Consider two disjoint events A and B in a sample space S. Which of the following is correct? 

Let A be the event that X ≥ 5 and let B be the event that X ∈ [3, 8]. The probability of A conditional on B is

Two women and four men are to be seated randomly around a circular table. Find the probability that the women are not seated next to each other. 

A number, say X₁, is chosen at random from the set {1, 2}. Then a number, say X₂, is chosen at random from the set {1, X₁}. The probability that X₁ = 2 given that X₂ = 1 is

Let X denote the absolute value of the difference between the numbers obtained when two dice are tossed. The expectation of X is: 

Let A be the event that X ≥ 5 and let B be the event that X ∈ [3, 8]. Events A and B are

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, then the number of outcomes B must have so that A and B are  independent, is

Two persons, A and B, shoot a target. Suppose the probability that A will hit the target on any shot is 1/3 and the probability that B will hit the target on any shot is ¼. Suppose A shoots first and they take turns shooting. What is the probability that the target is hit for the first time by A’s third shot?

Suppose 10 athletes are running in a race and exactly 2 of them are taking banned drugs. An investigator randomly selects 2 athletes for drug testing. what is the probability that neither of the cheaters will be caught?

Jai and Vijay are taking a exam in statistics. The exam has only three grades A, B and C. The probability that Jai gets a B is 0.3, the probability that Vijay gets a B is 0.4, the probability that neither gets an A, but at least one gets a B is 0.1. What is the probability that neither gets a C but at least one gets a B?

You've been told that a family has two children and one of these is a daughter. What is the probability that the other child is also a daughter?

In order to join the ‘Gamers Club’, Mr A must choose a box from the two identical boxes in a room, and draw one ball from the chosen box. All he knows is that both boxes are non empty, and have a mix of red and green balls. If the ball that he draws from his chosen box is green, he is admitted to the club. You are given two identical boxes, 50 red balls and 50 green balls and asked to allocate these balls to the two boxes in order to maximize in order to maximize Mr. A’s probability of being admitted to the club, given that he will choose a box randomly. If you allocate these balls correctly, the probability that Mr. A gets admitted to the club equals

A company has 100 employees, 40 men and 60 women. There are 6 male executives. How many female executives should there be for gender and rank to be independent?

If two balanced dice are rolled, the sum of dots obtained is even with probability

Suppose player 1 has 5 coins and player 2 has 4 coins. Both players toss al their coins and observe the number that come up heads. Assuming all the coins are fair, What is the probability that player 1 obtains more heads than player 2?

A fair coin is tossed until a head comes up for the first time. The probability of this happening on an odd-numbered toss is

A bowl contains 5 chips, 3 marked $1 and 2 marked $4. A player draws 2 chips at random and is paid the sum of the values of the chips. The player’s expected gain (in $) is

A budget line

Suppose that in a two commodity world, prices of the commodities as well as the budget of the consumer double. Following this

In a two commodity world the prices of the two commodities X1 and X2 are given at Rs.5 and Rs.7 respectively, to a consumer with a given budget. Suppose the commodities can be purchased and consumed in discrete quantities only. Each of X1 and X2  axis is found to contain a point that fully exhaust the consumer’s budget. Then, which of the following is true?

Suppose a consumer has $100 to spend on two goods, shoes and shirts. If the price of a pair ofshoes is $20 per pair and the price of a shirt is $15 each, which of the following combinations is unaffordable to the consumer?

A consumption point inside the budget line

If Price of Good 1 increases more than the increase in price of good 2 then

If Price of Good 1 increases more than the increase in price of good 2 then

Which of the following factors does not affect the slope and position of a consumer's budget line between two products, A and B?

The negative slope of budget line implies that

Which of the following describes what happens to a consumer's budget line if that consumer's budget increases? The budget line

Consumer A purchases Good X and Good Y. If consumer A s income and the prices of Good X and Good Y double Consumer A s Budget Line will:

Consider the budget line of a consumer that consumes only two Goods X and Y, with the quantity of Good X represented on the horizontal axis and the quantity of Good Y represented on the vertical axis. If money income is held constant, a rise in the price of Good X and a fall in the price of Good Y will: 

If there are two goods with positive prices and the price of one good is reducedwhile income and other prices remain constant then the size of the budget set is reduced

If good is measured on the horizontal axis and good is measured on the vertical axis and if the price of good is p1 and the price of good is p2 then the slope of the budget line is -p2/p1

If all prices are doubled and money income is left the same the budget set does not change because relative prices dont change

There are two goods You knowhowmuch of good a consumer can a ord if she spends all of her income on good If you know the ratio of the prices of the two goods then you could draw the consumers budget line without any more information

If there are two goods and the prices of both goods rise then the budget line must become steeper

If Good is on the horizontal axis and Good is on the vertical axis then an increase in the price of Good will not change the horizontal intercept of the budget line

If all prices double and income triples then the budget line will become steeper

If there are two goods and if one good has a negative price and the other has a positive price then the slope of the budget line will be positive

Investment increases proportionately with the increase in capital stock implies that, for a given rate of saving _______

In the Solow Model, The production function becomes __________ as k increases indicating that it gives _____________ marginal product of capital

The aggregate production function for the Solow growth model assumes (A) ___________ returns to scale and (B) _____________marginal productivity of labour and capital.

In the Solow Model, the point where investment is equal to depreciation is known as the ______________.

According to the Solow Model, _____________________ is a function of capital.

Consider an economy described by the following production function :

F(K, L) = K^0.5L^0.5  

Assume that the rate of depreciation is 10% per year and rate of saving is 30%. Find the steady state level of Investment of Solow’s model.

Consider an economy described by the following production function :

F(K, L) = K^0.5L^0.5  

Assume that the rate of depreciation is 10% per year and rate of saving is 30%. Find the steady state capital stock per worker of Solow’s model.

In the Solow Model, the change in saving rate produces

In the Solow Model, the economy which is not at steady state

In the Solow Model, at the steady state we have

In the Solow model, the steady-state level of capital per worker is determined by:

What is the "golden rule" level of capital in the Solow model?

In the Solow model, what role does the depreciation rate play in the economy?

The Solow model predicts that countries with lower initial levels of capital per worker will:

In the Solow model, technological progress is often considered to be:

According to the Solow model, if a country increases its saving rate, what will happen in the long run?

In the context of the Solow model, what is meant by "steady state"?

According to the Solow model, an increase in the population growth rate will:

Which of the following assumptions is NOT part of the Solow model?

In the Solow model, convergence occurs when: