Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness. Use with [mathematics]

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2
votes
2answers
234 views

Gambling game where you pick how many coins to flip

At a gambling joint, you are invited to be a player in a game with identical unfair but consistent coins flipped simultaneously in each round, with no cost to enter. Each player gets a different ...
8
votes
1answer
321 views

Probability that D wins this contest

Problem: $A, B, C, D$ are playing an archery game. They have equal probability of landing their arrow on any spot the target with radius of $R$. Their score is the distance to the center of the target....
0
votes
2answers
326 views

A certain 'Monty Hall' variant was played. How many doors were there, and, what was the value of the prize?

Recall the standard Monty Hall scenario where a presenter hides one prize with high value $h$ behind one closed door (e.g., in the classical version: the one high prize is a car), and, equal prizes ...
15
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6answers
3k views

Three horse race

There are three horses in the race. You know the following information about them: Horse A will finish the race in 50 or 60 seconds with both events being equally likely. Horse B will always finish ...
0
votes
2answers
138 views

How can we allocate when we have 150 open slots every day (5 days a week) for those 200 arrivals every day

My question is to solve a very basic problem related to the allocation of slots. Say there are 20 teams with 10 persons in each team. I have 150 open slots every day (5 days a week) for those 20 teams ...
4
votes
2answers
484 views

How many seats around the table?

This puzzle is very much inspired by a recent, excellent, one, posted here. If anyone, in particular the author of the other puzzle, prefers this one to disappear, I will immediately do so and I ...
3
votes
1answer
107 views

Two pairs of dice with the same probability [duplicate]

Alice has two dice each numbered from 1 to 6. Bob has two dice as well, the numbering is not known, but each face has a positive integer. The numbering on each dice can be different and a number can ...
4
votes
2answers
212 views

The Game of MIM

In the game of MIM, each of two players, Alice and Bob, receive a board as shown below: They are then dealt in turns one card from a shuffled set of cards numbered 0 through 9 which they must ...
24
votes
4answers
4k views

The "Loop of rope" dilemma

It's a "dilemma" that I encountered in real life problems. I believe that it's not new and is quite easy to explain, but may look puzzling at first glance. Alice and Bob are playing with a ...
3
votes
1answer
187 views

What is the most STAMINA-efficient strategy to escape the well?

You are roleplaying as an adventurer under the direction of a sadistic DM who has just thrown your character down a well. In order to escape, you have unlimited chances at a STAMINA check, difficulty ...
2
votes
2answers
236 views

Extension to the coin flipping puzzle

This is an extension to this great puzzle: Coin Flipping Puzzle. The main difference is we now have ternary sequences instead of binary sequences. Two criminals $A$ and $B$, were recently captured and ...
1
vote
1answer
221 views

Optimal parking at a concert

You are going to a concert. The road to the concert has 100 car parking spaces arranged in a straight line. The spaces are numbered from 1 to 100, where space 1 is in the beginning of your journey and ...
6
votes
1answer
811 views

Three cups and a ball

I am walking down the streets of Paris when a street performer approaches me. He has a row of 3 cups facing down on a table. He places a ball under the left cup. He proceeds to swap pairs of cups, ...
10
votes
2answers
507 views

How should you distribute the fighting power?

Alice and Bob both have N warriors under their command, numbered 1~N, and $1$ point of fighting power at their disposal. Before the game, they privately distribute the power between their warriors. ...
0
votes
2answers
166 views

Odds of there being two solutions to a word puzzle [closed]

What are the odds of there being two solutions to, say, a cryptoquote? And is anyone aware of an example of such?
6
votes
2answers
437 views

A three-way bet

Alice, Bob and Carole are playing a betting game. At the beginning, they have 20 chips in the common pot. They move alternatively in the order of Alice, Bob and Carole. In their move, a player ...
4
votes
3answers
699 views

Number of cards to be pulled

Ten cards, numbered 1-10, are randomly dealt to 2 players, A and B, such that each player gets 5 cards. Before the cards are dealt, player A will say a number N. After the cards are dealt, A will ...
12
votes
1answer
380 views

How should you bet?

Alice and Bob are playing a betting game. Each has 20 chips to start with. They move alternatively starting with Alice. In their moves, they name a number $n$ and toss a fair coin: if head, they get $...
9
votes
9answers
3k views

How many gold coins can you extract from the billionaire?

An eccentric billionaire plays a game with you. She has an urn with 100 gold coins. Each time, you can take any number of coins from the urn. If you take n coins, she will flip a fair coin. If head, ...
10
votes
4answers
1k views

Simulating a biased coin with an unbiased one

You are given an unbiased fair coin, ie., a coin that produces heads with probability 0.5. Can you use this coin to simulate a biased coin that produces heads with some given probability $p$ ? This is ...
26
votes
7answers
4k views

Simulating an unbiased coin with a biased one

You are given a biased coin. With probability $p$ it produces heads, where $p$ is in the range $(0,1)$. How can you use this coin to simulate an unbiased fair coin, ie., a coin that produces heads ...
3
votes
0answers
140 views

Slow & Fast drivers

Let us define "fastness" as a characteristic of how fast/agressive a driver is. One aspect of this is the (maximum) time between a traffic light turning red and the driver deciding they have ...
12
votes
3answers
1k views

Even odds from die with single mark

We want to make a close equivalent of a fair coin throw, by throwing an N-sided fair die T times. The catch: only one side is marked, by a colored disk on that side's center (like the traditional ...
23
votes
4answers
2k views

Which die should you choose?

You are playing a game with dice. You have a grid with 13 cells shown below. A token starts in the left-most cell (start). Each turn you roll an $n$-sided die and get a number $x$ between $1$ and $n$, ...
12
votes
3answers
790 views

Outmaneuver your opponents in the duel

A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
-1
votes
1answer
110 views

Blindly choosing a ball from a bag [closed]

You are blindfolded. You are handed a bag and told that there are three balls and two cubes, all of which are the same size and are equally likely to be chosen. You blindly choose one of the items ...
6
votes
2answers
706 views

Balancing the marble game (Red marbles are OP, please nerf)

Ash and Bree are playing a simple game of chance: They fill a bag with small marbles coloured red or blue. They take turns to draw a marble from the bag without looking, then: If Ash draws a red ...
2
votes
2answers
508 views

Lightbulbs in a 3×3 square

Suppose we have a $3\times 3$ arrangement of lightbulbs and we switch them on/off randomly (probability $½$). What is the probability the no adjacent bulbs are on? My attempt was: Let $1= $ on and $0 =...
1
vote
1answer
169 views

Variation of 100 prisoners [duplicate]

There are 100 prisoners, each prisoner is given a number between 1 and 100 without knowing which number, the number can repeat and not all of the numbers must be given. Each prisoner in his turn can ...
7
votes
9answers
3k views

"We accept 20% of candidates and I'm 90% good at my job..." [closed]

There is a famous investment firm where a partner was known for having candidates walk into the room without a greeting, sit across from him at a huge desk, and start right away by asking: "We ...
1
vote
2answers
247 views

Anne and Bernard's marbles

Anne and Bernard have between them 100 marbles, Anne the most. Some in each bag of their marbles are red, the rest, though fewer, are blue. If Anne draws at random two marbles from her bag of marbles, ...
7
votes
1answer
258 views

Stochastic Taxicab Path

A city's roadworks is laid out as a perfectly rectangular tiling. A commuter within this city has to travel to work a distance of 17 blocks east and 7 blocks north each day, and tries to take the same ...
0
votes
2answers
101 views

Car registration similarity [closed]

In my city, car registration plates contain 3 numbers (0 to 9) and 3 letters (A to Z). Today I've noticed that my neighbour's car has the same registration as my car except for one character. Should I ...
9
votes
5answers
461 views

The Two Envelope Game Show

This is an original riddle I made, heavily inspired by the Two Envelope problem. I have my answer to this problem, but (full disclosure) even I’m not 100% sure I’ve got it right. I post it half ...
19
votes
1answer
863 views

Honeybee Hangover

A drunken honeybee lands on a completely random hexagon of a large triangular section (depicted below) of its hive, and then every second afterwards, takes a step to a completely random adjacent ...
18
votes
1answer
570 views

Lap Theory Optimal Betting Game

Three prisoners are seated at a table. Each of them has a mobile phone on their lap, and they are not allowed to look at anyone else’s phone (and obviously no other form of communication is allowed). ...
9
votes
2answers
438 views

Three way duel, which guns to choose?

Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
12
votes
1answer
874 views

Lawbreaking by the numbers

Special Agent Benford has been stymied by a third unsolved case of miscreant creative accounting and will voluntarily retire from the Fraudulent Numbers Task Force. Benford’s ability to detect ...
10
votes
5answers
1k views

Two player Monty Hall variation

Alice and Bob are going on a game show as partners. In this game, there are three doors, which contain a car, the car keys, and a goat, which are arranged randomly and secretly behind the doors. Alice ...
6
votes
4answers
1k views

A bet with your friend

James, your friend, has invited you to bet with him. He has a fair die, with $3$ faces showing $0$ and $3$ faces showing $1$. You pay him $\\\$70$. He throws the die $15$ times, and records the sum of ...
-5
votes
1answer
163 views

You went to the casino again [closed]

You went to the casino again and saw a cardboard, with the following written on it: There are $\color{brown}{\text{dirt}}$ coins. Every time, you pay \$$10$. Then the coins will be thrown, and you ...
1
vote
3answers
176 views

Random sum adds to 1000 [closed]

A random whole number is generated between 1 and 1000 inclusive, and added to a sum. A new randomly generated whole number is generated and added to the sum until the total sum is greater than or ...
6
votes
5answers
1k views

Probability of three identical digits on a four-digit digital clock?

On a digital clock showing 00:00 to 23:59, what is the probability of having exactly three identical digits?
5
votes
4answers
375 views

A probably sunny Sunday

Besides this problem I also use the following one to rise the interest of my students on the Probabilities Theory. It's a funny puzzle were the use of simple arithmetic rules doesn't work. We have to ...
8
votes
1answer
142 views

Black-hat/white-hat logicians with a bell and a meal

At the 2020 yearly black- and white- hatted logician gathering, the following fun activity is organized. $N$ logicians will sit around a table, each wearing a black or a white hat the color of which ...
10
votes
1answer
532 views

Mathematics in adolescence

When I start to teach probabilities, I challenge my students with the following: Thelma is 16 years old and can only go out at night if one of her parents gives her permission. She knows her father ...
1
vote
0answers
71 views

Choose the single correct answer [duplicate]

If you choose an answer to this question at random, what is the chance that you will be correct? A. 25% B. 0% C. 50% D. 25%
3
votes
2answers
169 views

Broken stick riddle

There is a famous mathematical riddle called The Broken Stick Problem. Here’s the extension: If a straight stick is accidentally broken into three pieces, the probability of being able to form a ...
8
votes
4answers
679 views

Circle inside circle

Here's a fun little math problem I made(by fun I mean no complicated methods needed at all.) You have a large circle with radius N with a cross in it to seperate the 4 quadrants(so that the figure ...
6
votes
2answers
819 views

Exam statistics

250 teenagers gather for an exam. Peeking at the roll, a math-inclined among them note that if they are split into 10 groups of 25 per alphabetical order, then in each group, there are two with the ...

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