Questions tagged [probability]

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

Filter by
Sorted by
Tagged with
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
6answers
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
118 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 ...
22
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
744 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
101 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
673 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
497 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
147 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
232 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
249 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
98 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 ...
8
votes
5answers
434 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 ...
18
votes
1answer
838 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 ...
17
votes
1answer
526 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
379 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
856 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
158 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
169 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
358 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
2answers
259 views

Searching for the Covid vaccine

You have 1000 possible Covid vaccine candidates. You need to test them and find out if one works as quickly as possible. The test is to apply a small drop of a vaccine candidate to a sample, and ...
8
votes
1answer
128 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
517 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
67 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
153 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
610 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
810 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 ...
10
votes
3answers
331 views

Find a good strategy to survive the multiplayer duel

Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can ...
10
votes
3answers
3k views

Lottery strategy

In a city, the official lottery consists of scratch cards that cost 10 bucks each. Each scratch card contains 36 squares with a hidden number on each square : 21 of them are “zeroes”, 9 of them are “...
8
votes
2answers
859 views

Wait, it is worth it?

You went to a Casino, and saw a quite interesting stall. The cardboard besides the stall says: You first pay \$$5$ You have to toss the fair coin. If it lands heads, you can ...
16
votes
4answers
1k views

Random walking on a board

There’s a pawn starting in the center of this game board. At each move, it can advance randomly towards any of the adjacent squares sharing a common side with equal chance. What’s the probability of ...
0
votes
0answers
56 views

A Dices Probability Riddle [duplicate]

Bob (A), Steven (B) and Joe (C) were playing with dices, each one of them made his own dice and wrote a number between 1-6 on each side of his dice. After playing for a while they've noticed that : (...
1
vote
0answers
101 views

full unmatch probability [closed]

You have 5 distinct color envelops and 5 distinct color letters. You randomly put one letter in each envelop. What is the probability of no pair matching in color? I can find the answer with brute ...
8
votes
1answer
325 views

Frog in the Well [duplicate]

A frog is trapped in a well, just 1 meter below the lip. On sunny days, the well is dry, and the frog is able to climb up 1 meter. On rainy days, the well is wet and the frog slides down 1 meter. If ...
5
votes
1answer
162 views

Not a coincidence

Your company has successfully made 140 sales since they started promoting the new product. The other owner, who is very superstitious, notices that today is the 140th day of the year, and believes ...
5
votes
2answers
327 views

Achieve the best outcome by a tactical statement

This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
3
votes
1answer
195 views

Probabilities for “What number is that? — asks grandpa”

Inspired from Multilanguage generalization of "What number is that? Asks Grandpa" and What number is that ? Asks Grandpa In this puzzle we will use the English alphabet of 26 letters. We ...
2
votes
1answer
158 views

Ideal number of Fruit Baskets

I've been playing some Runescape lately and while training the "Thievery" skill, I encountered a little math question I would like to figure out: The mechanics are simple: One after the ...
7
votes
1answer
229 views

The sadistic chieftain and the lethal truel game

In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind. "I'll ...
8
votes
5answers
542 views

Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
9
votes
5answers
377 views

Find the optimal strategy for this dice game

You are playing a game: You have $6$ standard 6-sided dice that are all rolled at the start of the game. The sum of dice values is your score. Each turn, you can take any (or none) dice and reroll ...
6
votes
1answer
152 views

Darwin Fooling Dalton

Dalton wants to measure the effectiveness of a treatment for a particular type of plant and, being a good scientist, decides to have a control group that does not have the treatment. He is able to ...
1
vote
2answers
161 views

Cheapest strategy on average to find specific items in a set

The problem You have a set on N (around 15-30) seemingly-identical objects, which in fact comprises a small number D (unknown, between 1-3) of defective objects and the rest (N-D) are good. There is a ...
13
votes
4answers
1k views

Football Rivals

Team A and Team B are perennial football rivals. Every year they meet for a series of games. The first team to win four games gets to take home the Golden Teapot and keep it for a year. The teams are ...

1
2 3 4 5
7