ID 926

ID 943

Anna has 3 bags of marbles.

The first contains 5 white marbles and 5 green marbles.

The second contains 2 white marbles and 8 blue marbles.

The third contains 16 white marbles and 4 green marbles.

If she randomly selects a single marble from each bag, what is the probability that all three marbles will be green?

ID 944

Tom has 3 bags of marbles.

The first contains 4 white marbles and 6 green marbles.

The second contains 2 white marbles and 8 blue marbles.

The third contains 12 white marbles and 8 green marbles.

If he randomly selects a single marble from each bag, what is the probability that all three marbles will be white?

ID 959

ID 962

John has an average of 89 on his three math exams.

To earn an A, he must have a 90 average.

What is the lowest grade he must earn on the next exam to raise his average to 90?

ID 972

ID 977

How many different 7-digit phone numbers can be used by a phone company?

The phone numbers cannot start with a zero.

ID 982

The table shows the results of a competition among 5 teams.

Each team plays two matches against each of the other teams, with three points for a win, one point for a draw and none for a defeat.

How many draws were there?

ID 1044

As each of five eggs is weighed, the average weight increases by one gram each time.

If the first egg weighs 50 grams, what is the weight of the last egg?

ID 1095

The probability that two randomly chosen people in a big city are younger than 25 is 25%.

What is the probability that 3 randomly chosen people from the city are younger than 25?

ID 1116

In a game, you have a 1/5 probability of winning $100 and 4/5 probability of losing $26.

What is the most likely amount of money you will win (or lose) at the end of 1000 games?

ID 1174

ID 1281

John is sick 6 days per year.

The probability of being sick on a Saturday or a Sunday is two times less than on any other day.

What is the probability that John will be sick on a Monday?

ID 1312

The formula developed by Austrian mathematician Richard Von Mises shows the probability of at least 2 people from n having their birthdays on the same day of the week.

What is the probability that 2 people have their birthdays on the same day of the week?

ID 1314

Five people sit at a round table.

What is the probability that they sit in age order?

The order can be ascending or descending, clockwise or counterclockwise.

ID 1324

The formula developed by Austrian mathematician Richard Von Mises shows the probability of at least 2 people from n have their birthdays at the same day of the week.

What is the probability that at least 2 people from 7 people have their birthdays at the same day of the week?

ID 1342

A boy begins walking from his starting point. Each hour, he either walks one kilometer to the east or one kilometer to the north, but he never walks in the same direction.

In how many different ways can he get to a point that is 8 kilometers to the north and 8 kilometers to the east of his starting point?

ID 1350

ID 1369

Abbey has a dog Abby.

She places 5 tiles with the letters of her surname into a bag.

She picks up one tile after other without looking.

What word has the greatest probability of appearing in the correct order from the beginning?

ID 1395

Two princes and two princesses are ready to marry.

Everybody independently chooses a partner without telling anyone.

What is the probability that everybody chooses a person who chooses her/him?

Assuming that boys choose girls and girls choose boys.

ID 1410

I randomly place three crosses into different cells of the grid.

What is the probability that the crosses lie on the same straight line?

ID 1449

A 4-character password uses exactly two different digits.

Each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

How many such passwords are possible?

ID 1543

After a rodeo, four cowboys have a meeting in a saloon.

Each cowboy has only one bullet.

Each cowboy randomly chooses one of the other three cowboys and successfully shoots him.

What is the probability that all of them are shot?

The photograph courtesy of Roland Sauter

ID 1826

ID 1830

ID 1832

ID 1975

ID 2150

Make 727 by using three 7s.

You can use any math operator that you would like.

How many times do you use the plus sign (+) in the expression?

ID 2156

Anna (A), Bill (B), Cindy (C), and Daniel (D) work on a project.

(1) Together, A, B, and C can complete it in 10 days.

(2) Together, B, C, and D can complete it in 11 days.

(3) Together, C, D, and A can complete it in 12 days.

(4) Together, D, A, and B can complete it in 13 days.

Who is the best performer?

ID 2180

A venture capitalist has choosen to invest in only one of three start-up companies: A, B, or C.

I will make a lot of money if I invest in the same company, and will lose all of my money if I choose another company.

I decide to invest in company A and I inform the venture capitalist.

He assures me that he has not invested in company C.

What company do you recommend for me to make the investment?

ID 2190

How many different cubes can I make by using six different colors such that each face has a different color?

I can rotate the cubes.

ID 2196

In a venture investment fund, all investors continue to invest into a new start-up company until the company becomes a great success.

If the company fails, then the investor tries to invest into another company.

An investor stops investing if the last investment is successful.

The probability of success is 10%.

What is the total proportion of successful to failed start-up companies in the investment fund?

ID 2253

ID 2258

What is the probability that two dominoes drawn randomly from a standard set will match (will allow concatenation)?

ID 3165

Tom has 3 bags of marbles.

The first contains 4 white marbles and 6 green marbles.

The second contains 5 white marbles and 15 blue marbles.

The third contains 12 white marbles and 8 green marbles.

If he randomly selects a single marble from each bag, what is the probability that all three marbles will be white?

ID 3198

Alex received a 90 on his essay and a 80 on his final.

He got an 90 on class participation.

The essay counts as 30% of his grade.

Class participation counts as 20% of his grade.

What is his grade?

ID 3466

This picture shows the first five rows of Pascal's triangle.

What is the sum of the numbers in the eleventh row of the triangle?

ID 3511

What is heavier than a cumulus cloud, which is about 1 cubic kilometer in volume?

Water is 1000 times heavier than the same volume of cloud.

ID 3513

Eight bugs are at the eight corners of an equilateral cube.

Each bug randomly picks a direction and moves along the edge of the cube until the next corner.

What is the probability that none of the bugs will meet another?

ID 3514

ID 3524

A chess queen attacks all squares along its path horizontally, vertically and diagonally.

I would like to place at least 2 white queens and at least 2 black queens on a 5x5 chessboard, such that the queens on either side cannot attack any opposing queens.

What is the maximum number of queens I can place on the board?

ID 3542

We want to merge 4 companies into one large company.

How many ways are there to merge them?

PS: you can merge only 2 companies at once.

ID 3566

ID 3584

ID 3586

I want to find the smallest number divisible by 225 that consists of ones and zeros.

How many 1's are there in the number?

ID 3621

Place the cards into two boxes so that the probability of randomly drawing a card with the letter B is at its maximum.

I draw a card from a box.

What is the probability?

ID 3646

Alex possesses 52% of a business and the rest belongs to Bill.

They take Craig into partnership so that the three partners have an equal interest in the business.

Craig pays $100,000,000.

How do Alex and Bill split the money?

ID 3681

ID 3781

A player must match three different numbers chosen from the integers 1 to 30 in any order to win a lottery.

If a ticket costs $1, what is the largest possible prize so that the organizers make a profit (on average)?

ID 3801

The picture shows a subway map.

If it takes 3 minutes to go from one station to the next one and 3 minutes to change lines, what is minimum time required to go from A to B?

ID 3828

In a country, a baby is born every 5 seconds, a person dies every 45 seconds, and a new immigrant comes to the country every 20 seconds.

What is the rate of growth in the country?

ID 3845

This is a standard set of dominoes.

Choose 2 dominoes at random.

What is the probability that these two dominoes match: an end of one matches at least one of the ends of the other?

ID 3869

A concert includes 3 cello pieces and 3 piano pieces.

In how many ways can the program be arranged if a piano piece must come last?

ID 3914

Anna and Bill roll a six-sided die.

The first person to roll a six wins.

Anna rolls first, then Bill rolls the die.

If nobody wins, they change the order: Bill starts first and so on.

What is the ratio of Anna's and Bill chances?

ID 3949

You can throw as many darts as necessary at the board shown in the picture.

Some total scores are impossible to obtain, such as all numbers less than 9 as well as 10, 12, etc.

What is the highest whole number score that is impossible to obtain?

Inspired by David Pleacher

ID 4030

ID 4058

John threw 8 fair dimes and Mary 9 dimes.

What is the probability that Mary has more heads than John?

ID 4090

Estimate the total you pay if the meal costs $29, the tax is 5%, and the tip is at least 15%.

Round up the total.

ID 4121

John and I have a glass of milk.

He drinks half of it and then I drink half of what is left.

He drinks half of what is left and I do the same.

We continue until nothing is left.

What proportion of the initial amount of the milk did I drink in total?

ID 4165

Five students Anna, Bill, Craig, Daniel, and Eugene commute by bus. Every morning each student independently and randomly selects to board one of the 4 buses.

What is the average number of students in the bus that Anna chooses?

ID 4306

ID 4323

If the probability of observing a white car in 10 minutes on a motorway is 0.99999, what is the probability of observing a white car in 2 minutes?

ID 4341

ID 4371

ID 4416

The sum of the integers from 1 to 2,000 inclusive is 2,001,000.

What is the sum of the odd integers in the range?

This is a typical SAT question.

ID 4445

My car can travel 20 km on one liter of gas on the motorway and 12 km on one liter of gas in the city.

If 60% of my travels are on the motorway, the odometer shows 15,000 km this year, and the average price is $2 per liter how much do I pay for the gas this year?

ID 4509

A 512-page book weighs 800g to the nearest 10g.

What is the weight of 200 pages if the cover represents 20% of the book's weight?

ID 4544

ID 4563

The sum of N consecutive integers is S.

Which of the following equations gives the value of the first integer of the sequence?

ID 4573

Veryfast Airlines loses 20% of the luggage.

Gerry puts his three favorite toys in three different bags.

What is the probability that he no longer has any toys after flying with Veryfast Airlines?

ID 4596

ID 4659

95.8% of James' classmates have different numbers of hairs than he has.

How many students are there in his class?

ID 4683

A ball rebounds half of the height from which it is dropped in a sport hall.

It stops rebounding when the height is smaller than 2 mm (0.002 meter).

How many times does the ball rebound if it drops from your head?

ID 4796

When Jane plays against Gerry in her favorite game, the odds are 5 to 3 that she will win.

What is probability that she wins three games in a row?

ID 4800

ID 4815

James the Mathematician wants to find a partner for a serious relationship. He has his own scoring system. He talks with N out of 100 girls, rejects them and records the best score S. He decides to talk to all 100 girls, making a decision about each one immediately. Once rejected, a girl cannot be recalled. After that, he continues to talk to others and stops when the girl has a score better than S.

What number N do you recommend to the boy?

ID 4816

Steve wonders "Why don’t I have a girlfriend?" He uses the following information. There are 10,000 girls and women who live in his city, but only 5% of them are age-appropriate for him. A total of 50% have the required level of education, and he expects that 50% of the women in the selected group are attractive to him and he hopes that at least 20% will find him attractive too.

How many girls in his city are potential girlfriends?

Inspired by a scientific article by Peter Backus.

ID 4817

Gerry's income is seven-eighths that of Jane.

Gerry's expenses are seven-eighths those of Jane.

They spend less than they earn.

Jane promised to marry Gerry if he saves more than she does.

Who saves more money?

ID 4969

ID 5025

The cost of living increased in the first year and it decreased in the second year by the same value.

What was the annual percent change if the total two-year change was minus one percent?

ID 5073

I got a total of 120 by using five zeros and any mathematical operators.

How many plus signs "+" did I use?

ID 5078

If you choose an answer to this question at random, what is the probability that you will be correct?

ID 5085

ID 5095

I bought a 20'' (the diagonal size) laptop with the ratio of the screen width to the height 4 : 3.

How many pixels does it have if the specification declares that PPI (pixel per inch) is 200?

ID 5111

I throw a coin on a chessboard.

The diameter of the coin is a half of the side length of a small square of the chessboard.

What is the probability that the coin touches both light and dark colors?

I don't take into account the cases when the coin touches the border of the chessboard.

ID 5123

Gerry's favorite digit is 7.

What is the probability that there is at least one 7 in the three-digit registration numbers of the next two cars that pass by?

ID 5134

I put red and white chocolate candies into a bag.

I randomly took 2 candies, noted their colors, and put them back into the bag.

I made 100 tests and both candies were white in 50 cases.

What is the most likely minimum possible number of candies in the bag?

ID 5135

**Coin landing on its edge**

I flip a fair Swiss franc* and it falls in mousse**.

What is the probability that the coin stays on its edge after the mousse melts?

*One Swiss franc is about 1 USD; diameter 23.20mm , thickness 1.55mm, weight 4.4g.

During a coin toss, the coin is thrown into the air such that it rotates edge-over-edge several times.

**A mousse (French 'foam') is a prepared food that incorporates air bubbles to give it a light and airy texture.

ID 5148

I roll two dice, one with the left hand and one with the right.

If the left hand die gives an odd number, the overall score is zero.

If the right hand die gives an even number, I roll it again and again until it is odd.

The score is the sum of the two numbers, except for the previously mentioned case.

There are exactly 6 possible scores: 0, 3, 5, 7, 9, and 11.

What is the average score?

The problem was suggested by Leslie Green

ID 5180

Leslie Green asks:

Criminal gangs have been known to pay vagrants to search through people’s refuse to find useful information like bank statements, credit card statements, receipts and so forth. With such personal information the criminals can then pretend to be the householder and take out loans, buy things or do other bad things having stolen somebody’s identity.

Steve is fairly careful about shredding such documents, but about 5% of the time an important document slips into the refuse unshredded. Fortunately, unless he is being specifically targeted, it is pretty unlikely that somebody will be going through his refuse every week. Let’s put the odds at 1 in 1000 for each weekly collection.

Assuming that if Steve fails to shred a document, and if the criminals are searching his bins at that time, his identity will be stolen, what is the chance of that happening in a 10 year period?

ID 5216

Jane was a naughty little girl. When she used to play 2-dice games with her late grandfather she always used to cheat. Her grandfather would pretend not to notice that the dice had landed and that she quickly changed one of the dice to her advantage. Specifically, if it was her throw she changed the lowest die to a 6. If it was his throw she changed the highest die to a 1.

Over a long run of throws, how much bigger was Jane’s average score than her grandfather’s?

Author: Leslie Green

ID 5243

Gerry tosses 2 coins and Jane tosses 3 coins.

What is the probability that Jane has more heads than Gerry does?

ID 5266

There are 9 houses on a street. The distance between any two adjacent houses is the same.

There is 1 child living in house number 1, two children living in house number 2, and so on. Nine children live in the house number 9.

If the school bus can only make one stop on that street, in front of which house should the bus stop so that the sum of walking distance among all children will be minimum?