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Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

40
votes
11answers
7k views

3 doors, three guards, one stone

You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want ...
15
votes
5answers
629 views

Blindfold Bingo

Congratulations, you have been selected from among the audience to compete in the fabulous Blindfold Bingo challenge! (cue annoying, yet catchy theme music.) Here you see our perfectly ordinary Bingo ...
3
votes
2answers
167 views

100 prisoners' names in boxes, against smart warden

My question, which I do not know the answer to, concerns the classic 100 prisoners and 100 boxes puzzle, summarized below. The solution to this assumes the names are placed in boxes randomly, and gets ...
41
votes
4answers
2k views

Hamlet and the theatre

Hamlet is preparing a play to find out the truth about his father's death. The theatre has $2015$ numbered seats and can contain all the members of King Claudius's court. He gives to each member a ...
15
votes
5answers
2k views

Monty Hall variation

During a train trip I cooked up a semi-autobiographical variation of The Monty Hall problem for people who already know the original. Perhaps it is more of a meta-puzzle than a puzzle, but I hope it ...
34
votes
3answers
5k views

Do better than chance

You and an opponent are playing the following game: Your opponent picks two different real numbers, however he wants to, and writes them on two cards, which he presents to you face down You choose ...
5
votes
1answer
728 views

How many cookies does someone need to grab to be certain to obtain a flavor?

I often found this riddle in many exams but I got often confused on how to tackle it. While it involves maths. I wonder if there is a subtle or a more layman method to obtain an answer using common ...
8
votes
3answers
1k views

A first choice die

You and your friend have met to play a game of dice. This is a very simple game where both players roll a die at the same time, and the player with the lower score pays a coin to the other player. In ...
4
votes
1answer
135 views

Minesweeper challenge #5

Coming back to another Minesweeper challenge... I've run into another "unsolvable corner" (corner of a puzzle where there isn't enough information to be 100% certain that any particular square that ...
1
vote
4answers
1k views

Birthdays on Consecutive Days

You are allowed to select as many random1 people as you like, and place them in a room. How many do you need for the probability that at least 2 people will have a birthday2...   a. on the ...
9
votes
5answers
1k views

How long will my money last at roulette?

I'm at the casino, standing next to a roulette table with a \$10 minimum bet. I want to stay here as long as possible, so I'm going to repeatedly make the minimum bet until I run out of money. I'm ...
5
votes
5answers
3k views

This Website Needs More Cat Pictures?

I love cats! And I love browsing cat pictures! :3 I stumbled on a webpage that shows random cat pictures every time I refresh the page. (For example, this site.) It has a database of $N$ cats ...
1
vote
1answer
78 views

Meeting of 2 Drunk Walkers (Random Walk) [closed]

There are 2 drunk guys who walks according to a Random Walk. Each of them, with equal probability of $ 0.5 $ turns either right or left. They both start at the origin and their turns are synchronized ...
5
votes
6answers
352 views

A Gambling Problem You Would Love To Have

Let's play a quick gambling game You are going to start by betting a penny, and then I roll a 10-sided die. It is labeled 0 through 9. Whatever you roll, that's what I multiply your bet by and give ...
5
votes
1answer
98 views

Puzzle creation problems using unbounded unknown numbers

I occasionally see puzzles that include language like this: You go to buy a specific car, whose fair price we’ll call N. You have absolutely no idea what N is Or this from the same site: Given ...
19
votes
8answers
2k views

A Short Dice Puzzle

There are $2$ fair dice: An $11$-sided die, valued from $-5$ to $5$, A $41$-sided die, valued from $-20$ to $20$. You pick one, and I'll take the other one. We roll the dice, and whoever rolls the ...
4
votes
4answers
2k views

A Short Dice Puzzle II

A standard $6$-sided die is put inside a cup. The cup is shaken and put upside-down, hiding the die. You are going to guess what is the number on the top of the die. But, instead of given $6$ ...
15
votes
3answers
2k views

The Sphinx's Dice

"I'm bored of riddles, I'm going to ask you a question about dice instead", says the Sphinx. "Now, I've got this set of Efron Dice here. There's four dice, and they have these values on their faces:" ...
4
votes
2answers
163 views

Optimal guess in a game

Suppose that A and B play a strange game. At the beginning of the game A can choose one real number - $x$ - between $0$ and $60$. Each round of the game goes like this: B names random real number $b$ ...
4
votes
0answers
195 views

Will you win the game?

You play a gambling game. On 100 folded pieces of papers are written 100 different values. You cannot see the numbers written on the folded pieces of paper, which are grouped in a pile. You pay 10 ...
10
votes
1answer
2k views

Lost first game – can I still make my mother proud?

I am one of the greatest finger wrestlers of my generation. Only 0.1% of all players are better. When I play against someone who's worse than me, I win 99% of the time. Against someone who's ...
6
votes
3answers
414 views

Monty's Labyrinth

(A fun combination of two classic puzzles, hope seasoned puzzlers enjoy.) Having escaped through almost all of a labyrinth, you are met by three magical doors. Two of them lead to certain and ...
4
votes
2answers
141 views

Probability in Fighting Tournament in which Contestants consume each other

A tournament has 2 teams of 24 people each of weight 1. Each team sends one person into the pit where they fight until one consumes the other taking on all their weight. The probability that one ...
15
votes
2answers
474 views

“Musical chair” for clock hands

A colleague and me usually make bets on the time when a simulation is finished. Next time I would suggest the following: At the time the simulation is finished we take a look at the analog clock on ...
13
votes
5answers
1k views

Olivia's cookie jars

Olivia loves cookies so much that Dad promises to buy her two cookie jars on one condition: that she only eats one cookie per day. Olivia agrees, and now two black, large cookie jars rest on the ...
10
votes
3answers
624 views

Fight Battle 21

Based off a very, very well-known puzzle The new RPG, Fight Battle 21, is now here! Now with the same three characters as the previous 20 editions! Knight: 6 HP, 60% chance to deal 3 damage Archer: ...
2
votes
2answers
91 views

Risk Appetites - betting percentages

This question is from the September/October issue of the Actuarial Review magazine. Kim and Ann start with an equal amount of money, but they value money very differently. Kim acts to maximize the ...
61
votes
15answers
9k views

2 Monkeys on a computer [closed]

(a) Two monkeys are typing capital letters (A-Z) randomly. The first stops typing when the word COCONUT appears as seven successive letters. The second stops typing when TUNOCOC appears; TUNOCOC is ...
12
votes
7answers
3k views

Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon $...
0
votes
1answer
120 views

Minesweeper challenge #4

While solving another Minesweeper puzzle, I ran into yet another unsolvable corner. Well, actually, this time I have two unsolvable corners in the same puzzle. Here's the bottom left corner: ...as ...
6
votes
5answers
2k views

A chess board and a coin! [closed]

You have a standard chessboard, consisting of $64$ squares ($32$ white and $32$ black) each of dimensions $4\times4$ cm, and you have a standard coin of $2$ cm diameter with tail and head. You flip ...
1
vote
1answer
97 views

Minesweeper challenge #3

I seem to have run into yet another "unsolvable corner" while playing Minesweeper. The following segment is taken from the bottom right corner of the puzzle. There are 5 mines remaining, and all ...
6
votes
5answers
2k views

Ten targets you need to hit

You are a good sniper and there are 10 targets you need to hit. The chance of hitting any target is the same. Strangely, with your accuracy the chance of getting 8 hits is equal to getting 7 hits in ...
4
votes
2answers
200 views

Minesweeper challenge #2

Again, I seem to have run into another situation where there doesn't seem to be a definitive set of squares to tap to solve a Minesweeper puzzle. What squares should I tap to maximize my chances of ...
3
votes
2answers
184 views

Is there a definite answer to this Minesweeper puzzle? If not, which square has the best chance of being safe?

I was working on solving an Expert puzzle in Minesweeper, but came across a hurdle in this corner (the top left). Is there a definitive solution to the problem? If so, what is it? If not, which ...
12
votes
5answers
1k views

Triangle in a circle

Suppose three points are chosen at random in a circle. A triangle is made with these three points as vertices. What's the probability that the triangle contains the origin of the circle? (Although I ...
-3
votes
1answer
92 views

max possible number of dice throw [closed]

Scott repeatedly rolls a pair of standard six-sided dice and keeps track of the sum of the two numbers rolled each time. So far he has not rolled any sum twice. What is the maximum possible number of ...
6
votes
1answer
192 views

Get 20 points from a target board

A target board consists of four parts, and each part has different numbers on it. You will make at most $10$ shots, and every shot's point will be added to your score. If you get a score of $20$ ...
12
votes
3answers
341 views

Guffin factory regulated heist

I work at a guffin factory. I manufacture guffins and have an unlimited access to guffin storage. I can fit up to 20 guffins in my bag, get them home from the factory and nobody will chase me. You ...
4
votes
6answers
5k views

100 pieces 1 opportunity, choose wisely!

Say you have a cake that is cut into 100 pieces. One of the pieces has a hidden prize. 100 people take turns, each taking a piece in sequence hoping to find the prize. Note: I slightly modified (...
5
votes
3answers
339 views

Probability of Girl or Boy

Suppose that I have a friend whose name is X. X has an elder brother who got married 10 years before. But X being a silly guy has the habit of forgetting things; you can say a “Short time memory loss”....
4
votes
2answers
135 views

3 points on a circle [duplicate]

There is a circle where you put 3 points randomly on it as shown below: What is the chance of these randomly chosen three points passing on an half circle? Reference: Bilim Teknik Dergisi 2018-07
13
votes
4answers
3k views

A dice game, what is the optimal strategy?

Alice was walking on the street when she came across a man playing with a die. She could not help trying to check if the die was loaded and while she was concluding that it wasn't loaded, the man ...
10
votes
7answers
444 views

A cooperative guessing game - Guess your order and card

6 players sitting in a circle and each assigned a card among 2 Hearts, 3 Hearts, ..., Ace Hearts (i.e. any of the Hearts cards). Holding her card above his forehead (i.e. Indian Poker fashion), each ...
3
votes
0answers
108 views

Variation of Boy/Girl Birth Problem [closed]

Parents keep having children until they have one girl, at which point they stop; and babies are girls with probability 0.49. If we select a child uniformly at random (from the entire population of ...
4
votes
1answer
224 views

How likely is a comeback in basketball?

For this most recent NBA season, ESPN.com has had in-game win probabilities: My question: Say a team gets a big lead and has a 90% chance of winning. What is the probability that at some point ...
5
votes
3answers
484 views

Foolproof double betting

Just made up a problem. Have ideas, but no proof yet – came here for professional help. Tonight an important match of Metagame (box/football/baseball/chess) takes place. Everyone is hyped. Everyone ...
8
votes
5answers
396 views

Two person game, choosing an integer between 1 and 30?

Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
1
vote
2answers
217 views

What are the chances on watching the clock? [closed]

This is a relatively straightforward little puzzle, but the answers are somewhat unintuitive or can prompt a new perspective. It might be an interesting little puzzle for a probability teaching ...
-4
votes
1answer
173 views

Bad mouse, good mouse [closed]

In a certain city, there are only two companies (called Company A and Company B), that manufacture computer mice. The computer mice from Company A last $x$ hours before needing to be recharged, ...