ID 862

Statistics, Data Analysis and Probability K11Five percent of the marbles in a jar are black.
One fourth of the marbles are green.
One half of the marbles are yellow.
The rest are white.

If there are 16 white marbles, how many marbles are in the jar?



ID 883

Statistics, Data Analysis and Probability K11A bag contains 6 green, 5 gray, and 4 violet marbles.

If 2 marbles are drawn at random from the bag, what is the probability that the marbles drawn are green?



ID 890

Statistics, Data Analysis and Probability K11If two dice are rolled 72 times, how many times is the sum of the two top numbers expected to be 12?



ID 899

Statistics, Data Analysis and Probability K11A city hall contains 165 chairs. The first row has 10 chairs.
Each additional row has one more chair than the row before it.

How many rows are there?



ID 900

Statistics, Data Analysis and Probability K11Which number could be removed from the set without changing the average (arithmetic mean of all the numbers)?



ID 907

Statistics, Data Analysis and Probability K11The first person is 100 cm tall.
Each next person is 20% taller than the person before.

Who will be taller than 2 meters first?



ID 986

Statistics, Data Analysis and Probability K11Five students put their sandwiches into five paper bags.
The bags are randomly distributed to the students.

What is the probability that exactly 4 students receive the correct bag?



ID 989

Statistics, Data Analysis and Probability K11Four kinds of apples are combined in a box.
I select apples from the box without looking.

How many apples must I draw to be sure of getting at least three of one kind?



ID 1019

Statistics, Data Analysis and Probability K11Alex received a 70 on his essay and a 90 on his final.
He got an 80 on class participation.
The essay counts as 30% of his grade.
Class participation counts as 20% of his grade.

What is his grade?



ID 1035

Statistics, Data Analysis and Probability K11Statistics show that for every 100 babies born in Funny Town, there are 10 more boys than girls.

What is the probability that Mr. Smith's newborn twins are boys?



ID 1266

Statistics, Data Analysis and Probability K11John arrives at a crossroad A from the North.
He makes four moves each time randomly choosing one of three directions.
For example, he could be at point B.

What is the probability that he finds himself at point A?



ID 1277

Statistics, Data Analysis and Probability K1199 numbers have an average of 101.
Ninety of these numbers have an average of 100.
What is the average of the other nine numbers?



ID 1278

Statistics, Data Analysis and Probability K11The average of a set of 12 numbers is 1.

If 18, 50 and -20 are added to the set, what is the new average?



ID 1318

Statistics, Data Analysis and Probability K11Anna has a bag with 90 wafers.
She eats 14 wafers on the first day.
Every day, she eats one wafer less than the day before.

In how many days does she eat all the wafers?



ID 1360

Statistics, Data Analysis and Probability K11Bobby takes five tiles with the letters of his name and places them into a bag.
He randomly picks one tile after another from the bag, and does not replace them in the bag.

What is the probability that he chooses the tiles in the same order as his name?



ID 1380

Statistics, Data Analysis and Probability K11Six standard dice are rolled and the numbers on the top faces are added together.

What sum is the most probable?



ID 1394

Statistics, Data Analysis and Probability K11Two princes and two princesses are ready to marry.
Everybody independently chooses a partner without telling anyone.

What is the probability that at least one princess chooses a prince that chooses her?

Assuming that boys choose girls and girls choose boys.



ID 1460

Statistics, Data Analysis and Probability K11The sum of N consecutive integer numbers is 2090.
The smallest number is 101.

Find N.



ID 1522

Statistics, Data Analysis and Probability K11I have eight dimes; five are real, and three are fake.
Whenever a real dime is flipped, it comes up heads with a probability of 0.5.
A fake dime comes up heads up with a probability of 5/6.

What is the probability that a randomly chosen coin will come up heads?



ID 1523

Statistics, Data Analysis and Probability K11A team of three children, Anna, Bill and Cindy, independently answers true-or-false questions.
Anna answers 90% of the questions correctly.
Bill and Cindy answer 50% of the questions correctly.
The answer is accepted as the team's response when the children give the same answer.
If their answers are different, then the result is ignored.

What is the probability that a team response is correct?



ID 1529

Statistics, Data Analysis and Probability K11Dueling Idiots Problem: three idiots participate in a duel.
They shoot at the same time.
If each idiot randomly chooses one of the other two idiots and successfully shoots him, what is the probability that at least one idiot will survive?



ID 1605

Statistics, Data Analysis and Probability K11There are 10 girls and 10 boys in a class.

A teacher randomly chooses two students.

What is the probability that they are a boy and a girl?



ID 1609

Statistics, Data Analysis and Probability K11Two dice are thrown.
You can see all 12 numbers except 2 faces that are on the table.
All the numbers on the ten visible faces are added.

Which sum of the numbers on the faces is best to bet on?



ID 1620

Statistics, Data Analysis and Probability K11A chip is placed at the bottom left corner square of a 5 x 5 grid.
The chip is moved one space upwards or to the right. One of the directions is randomly chosen, for example, by flipping a fair coin.

Find the probability that the chip reaches the center square of the grid in 4 moves.



ID 1671

Statistics, Data Analysis and Probability K11After a gun is fired in a saloon, 75% of the cowboys have a wounded ear, 80% have a wounded eye, 85% have a wounded arm, and 90% have a wounded leg.

What is the smallest percentage possible of cowboys who have all four wounds?



ID 1672

Statistics, Data Analysis and Probability K11If we set out by ranks of 10, we will be one short.
We will also be one short if we set out by ranks of 9, 8, 7, 6, 5, 4, 3, and even 2.
Yet there are fewer than 5000 participants.

How many are we?

Source: Marie Berrondom, Mathematical Games, 1983



ID 1675

Statistics, Data Analysis and Probability K11It takes 2 cards to build 1 floor of a card house.
It takes 7 cards to build 2 floors of a card house.
It takes 15 cards to build 3 floors of a card house.

How many cards does it take to build a 10-story house?



ID 1754

Statistics, Data Analysis and Probability K11Anna earned an average of 80% on her four exams.

If she never earned more than 90% what is the lowest possible percentage score she could have received in any one of the exams?



ID 1829

Statistics, Data Analysis and Probability K11What is the average of the smaller of two random numbers from 0 to 1?



ID 1968

Statistics, Data Analysis and Probability K11John answered 100 4-option multiple-choice questions.
He is sure that he correctly answered 50% of the questions.
In 30% of the questions, he chose the answer among two options, and he answered all other questions by randomly guessing among the four options.

What score does John expect to receive on the exam?



ID 1995

Statistics, Data Analysis and Probability K11Forty non-zero positive numbers are written in a row.
The average of the first two numbers is 1.
The average of the second and third numbers is 2.
The average of the third and fourth numbers is 3 and so on.

What is the last number in the row?



ID 2018

Statistics, Data Analysis and Probability K11This picture shows the first five rows of Pascal's triangle.
What is the sum of the numbers in the 10th row of the triangle?



ID 2033

Statistics, Data Analysis and Probability K11San Jose Scrabble® Club No. 21 published a three-letter word list that included 1014 English words.

Estimate the percentage of these words compared with all possible three-letter combinations?



ID 2157

Statistics, Data Analysis and Probability K11In a city, there were seven bridges.
There was a tradition to walk and cross over each of the seven bridges.

If a person starts and finishes at the same point, what is the smallest number of crossings the person would have to make?



ID 2213

Statistics, Data Analysis and Probability K11An entrepreneur wants to hire the best person for a position.
He makes a decision immediately after the interview.
Once rejected, an applicant cannot be recalled.
He interviews N randomly chosen people out of 100 applicants, rejects them and records the best score S.
After that, he continues to interview others and stops when the person has a score better than S.

What number N do you recommend to the cruel man?



ID 2256

Statistics, Data Analysis and Probability K11 A group of kids with dogs go for a walk.
There are 49 feet and heads altogether.
There are more dogs than kids.

How many dogs are there?



ID 3125

Statistics, Data Analysis and Probability K11Bob is rolling two dice and will subtract the second number from the first number.

What result is Bob most likely to roll?



ID 3128

Statistics, Data Analysis and Probability K11The average of twelve numbers is 8 and the average of another set of eight numbers is 12.

What is the average of all these numbers?



ID 3129

Statistics, Data Analysis and Probability K11Fifteen numbers have an average of 10.
Five of these numbers have an average of 5, four other numbers have an average of 4, three an average of 3, and two an average of 2.
What is the remaining number?



ID 3131

Statistics, Data Analysis and Probability K11The average (arithmetic mean) of a set of 10 different numbers is 98.
If the numbers 40 and 140 are removed from the set, what is the average of the remaining numbers?



ID 3164

Statistics, Data Analysis and Probability K11Anna 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 white?



ID 3175

Statistics, Data Analysis and Probability K11John has an average of 87 on his two 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 3177

Statistics, Data Analysis and Probability K11I roll two dice.

What is the probability that the two numbers are equal?



ID 3195

Statistics, Data Analysis and Probability K11Everyone in tenth grade classes voted on a motion.
Sixty percent of the girls voted YES.
Forty percent of the boys voted YES.
The motion passes if over 50% of the votes are YES.

In what class the motion was rejected?



ID 3197

Statistics, Data Analysis and Probability K11Alex received a 60 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 3240

Statistics, Data Analysis and Probability K11Gerry and Jane are younger than 25.

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

What is the probability that 4 randomly chosen people from the city are younger than 25?



ID 3247

Statistics, Data Analysis and Probability K11Jane and Gerry visit a casino.

In one game, they have a 1/5 probability of winning $100 and 1/2 probability of losing $50.
They have also a chance of no win / no loss.

What is the most likely amount of money they will win (or lose) at the end of 100 games?

Gambling is bad!



ID 3338

Statistics, Data Analysis and Probability K11John is sick 12 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 3374

Statistics, Data Analysis and Probability K11Abbey 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 3484

Statistics, Data Analysis and Probability K11John sent an email to his three partners.
Everybody answered and copied the answer to all others.
A total of 12 emails were sent.

How many emails are sent if there are 20 people communicating in the same manner?



ID 3492

Statistics, Data Analysis and Probability K11An average baby is about 20 inches (51 cm) long and weighs approximately 6 to 9 pounds (2700 to 4000 grams).

How many times heavier than a baby is an adult?



ID 3493

Statistics, Data Analysis and Probability K11The binary numeral system represents numeric values using two symbols: 0 and 1.

How is the number 999 written in binary code?



ID 3510

Statistics, Data Analysis and Probability K110 2 6 12 20 . . .
What is the 100th number in the series?



ID 3516

Statistics, Data Analysis and Probability K11If 2 salesmen can sell three luxury cars in 4 days, how many luxury cars can five salesmen sell to six clients in 7 days?



ID 3531

Statistics, Data Analysis and Probability K11If you are a redhead you have more than the average amount of hair.

This statement is . . .



ID 3540

Statistics, Data Analysis and Probability K11If the probability of an accident occuring in 4 years is 0.9999, what is the probability of an accident occuring in 1 year?



ID 3565

Statistics, Data Analysis and Probability K11Find the sum of the series:

1/2 + 1/4 + 1/8 + 1/16 + . . .



ID 3606

Statistics, Data Analysis and Probability K11Alex(A), Beatrice (B), and Craig (C) work on a project.

(1) Together, A and B can complete it in 10 days.
(2) Together, B and C can complete it in 12 days.
(3) Together, C and A can complete it in 15 days.

If Alex does it alone, how many days will it take?



ID 3745

Statistics, Data Analysis and Probability K11I ask you to pick a number from 1 to 100.
I then ask you, “Is the number greater than X?”
You must truly answer yes or no until I tell you the number.

What is the maximum number of questions I ask you if I choose the optimal strategy?

Here X is the number of my choice.



ID 3772

Statistics, Data Analysis and Probability K11Guesstimation

A man can jump up to four times the length of his own body.
Frogs can jump up to fifty times their length.
A flea can jump 350 times the length of its own body.

What is the average length of these three jumps?



ID 3780

Statistics, Data Analysis and Probability K11Alex must match three different numbers chosen from the integers 1 to 33 in any order to win a lottery.
He bought 333 tickets, each with a unique combination of numbers.

What is the probability of winning?



ID 3827

Statistics, Data Analysis and Probability K11In the United States, the average life span is 65 years and the average female gives birth to 2.6 children.
The average age when a female bears children is less than 30.

How many descendants would the female have at the end of her life?



ID 3944

Statistics, Data Analysis and Probability K11What is the average of all positive integers less than 100 that are multiples of 7?



ID 3961

Statistics, Data Analysis and Probability K11Which year has had the greatest number of Roman numerals in it?



ID 3974

Statistics, Data Analysis and Probability K11Which result ends in exactly seven zeroes.

Remember: N! = 1 x 2 x . . . x N



ID 4037

Statistics, Data Analysis and Probability K11After a test of a code, John detected 2 errors and Mary discovered 3 errors in the same code.
There is one error in common.
Estimate the number of errors that are still undetected.



ID 4082

Statistics, Data Analysis and Probability K11John and Mary have equal chances of winning.

What is more probable?



ID 4095

Statistics, Data Analysis and Probability K11After a 20% discount and 8% tax, a set of tin solders costs $540.

What was the original price of the set?



ID 4240

Statistics, Data Analysis and Probability K11Every day, a stock price of $444 is either increased or decreased by 4%.

When can it be $444 again?



ID 4351

Statistics, Data Analysis and Probability K11One bag contains two white marbles, another bag contains two black marbles, and a third bag contains one white marble and one black marble.
I pick a random bag and take out a black marble.

What is the probability that the remaining marble from the same bag is also black?



ID 4372

Statistics, Data Analysis and Probability K11A school offers the following dinner choices:

First course: soup or small salad;
Main course: vegetarian, chicken, pizza, cheeseburger or fish;
Dessert: apple cake, doughnut, fruit salad, ice cream or milkshake.

How many school dinners will I have eaten before I have to choose a combination that I have already eaten?



ID 4419

Statistics, Data Analysis and Probability K11The average IQ of 100 students is 101.
If the first ninety-nine students each have an IQ of 100, what is the IQ of the last student?



ID 4442

Statistics, Data Analysis and Probability K11Anna spent 120 Swiss francs in a Swiss souvenir shop. She was charged an extra 2% for paying with her credit card.

How much did she spend in USD?

Use an exchange rate of $1 = 0.96 Swiss Franc



ID 4476

Statistics, Data Analysis and Probability K11What is the probability of getting blue?



ID 4477

Statistics, Data Analysis and Probability K11What is the probability of not getting blue in two runs?



ID 4486

Statistics, Data Analysis and Probability K11If the first President of the USA George Washington took office in 1789 and the fortieth President Roland Reagan completed his duty in 2004 what is average duration of the term for the American Presidents?



ID 4499

Statistics, Data Analysis and Probability K11Javier Sotomayor (Cuba) is the men's record holder with a jump of 2.45 m set in 1993, the longest standing record in the history of the men's high jump.

Javier is 1.95 m tall.

What percentage of his height did he jump?

Data source : Wikipedia



ID 4510

Statistics, Data Analysis and Probability K11Bob used to weigh 100kg.
His new stressful job causes him to lose 10% every month.

How much does he weigh after 3 months of work?



ID 4566

Statistics, Data Analysis and Probability K11How many 9s are there in the result of the multiplication:

12345 x 99999 ?

Don't use the calculator.



ID 4570

Statistics, Data Analysis and Probability K11John's family tree includes 10 generations.

What is the minimum number of people on his family tree if there were no intermarriages?



ID 4584

Statistics, Data Analysis and Probability K11A line containing 9 keyboard letters on Gerry's laptop does not work.

If his password consists of 2 letters, 4 numbers, and 1 special symbol, what is the probability that he will be able to log in?



ID 4766

Statistics, Data Analysis and Probability K11Gerry estimates that two angles of a triangles have a measure between 50 and 70 degrees each.

If this is true, what would be estimate for the third angle?



ID 4770

Statistics, Data Analysis and Probability K11What is the difference between 11 in decimal (normal) and binary systems?

A binary number is made up of only 0s and 1s.



ID 4808

Statistics, Data Analysis and Probability K11What time is it 1234 minutes after 1:23 a.m.?



ID 4839

Statistics, Data Analysis and Probability K11There are 800 students in a school.

The students' average age is 12 years and 60% of them are girls.

What is the difference between the sums of girls and boys ages?



ID 4849

Statistics, Data Analysis and Probability K11How many times do you expect to get 5 if you throw a die 55 times?



ID 4950

Statistics, Data Analysis and Probability K11If you toss a dime five times and it lands heads up three times, what are the chances it will land heads up if you toss it again?



ID 4970

Statistics, Data Analysis and Probability K112 + 2 = 11
In what numeral system is the expression true?



ID 4984

Statistics, Data Analysis and Probability K11The masses of sugar and water in my 200 g tea cup are in the ratio 1 : 9.

If I drop two 25 g cubes of sugar into the cup, what will be the new percentage of sugar?

(We assume that the cup does not overflow in the process!)



ID 4988

Statistics, Data Analysis and Probability K11Which of the following could be the percentage of even numbers among several consecutive integers?



ID 4990

Statistics, Data Analysis and Probability K11What is the sum?

2001 + 2002 + . . . + 2099



ID 5024

Statistics, Data Analysis and Probability K11The cost of living increases uniformly by 44% in a period of two years.

What is the annual percent increase?



ID 5031

Statistics, Data Analysis and Probability K11If I roll two dice, what is the probability of rolling a six on at least one of them?



ID 5056

Statistics, Data Analysis and Probability K11You are rolling two dice and adding the numbers on the top faces.

What sum is better to bet on if you have no other choices?



ID 5087

Statistics, Data Analysis and Probability K11What is the sum of the first 13 numbers that are evenly divisible by 13?



ID 5121

Statistics, Data Analysis and Probability K11Gerry and Jane like to look at registration plates of cars that pass by.

They add the three digits and bet on a result.

Among the values below, what is the best sum of three digits to bet on?



ID 5133

Statistics, Data Analysis and Probability K11If I put these balls in a bag and take two balls without looking, what is the probability that the two balls are white?



ID 5147

Statistics, Data Analysis and Probability K11I 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 probability of a score of 3?


The problem was suggested by Leslie Green



ID 5157

Statistics, Data Analysis and Probability K11Buy 2 for the price of 3 and get 50% off!


What is the final rebate do you get?


'Buy, buy, says the sign in the shop window; Why, why, says the junk in the yard.' - Paul McCartney



ID 5193

Statistics, Data Analysis and Probability K11The pie chart shows the number of men, women and kids in a county.

What is the ratio of children to women?



ID 5244

Statistics, Data Analysis and Probability K11Gerry tosses a coin and Jane tosses 2 coins.

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



ID 5251

Statistics, Data Analysis and Probability K11Martin has ten thousand dollars in a bank account. The interest rate for his account is 10% every year.

How much money will Martin have in his bank account after three years?



ID 5258

Statistics, Data Analysis and Probability K11Jane and Gerry compete in a best-of-three match.

If Gerry plays so that his girl-friend has a 60% chance of winning any particular game, what is the likelihood that she will win the match?



ID 5278

Statistics, Data Analysis and Probability K11Cletus is absolutely, definitely, the worst student the driving school has ever seen. When asked to drive at a steady speed he constantly accelerates too hard, overshoots the target speed, and then brakes too heavily. He has what the instructors call a "heavy foot".

By some miracle he manages to always hit the same top speed of 20 mph before braking in a continuing non-repeating pattern like the one shown.

What is his average speed?

Author: Leslie Green