Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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Place 10 Coins Heads Up Blindfolded [duplicate]

You are blindfolded and 10 coins are placed in front of you on table. You are allowed to touch the coins, but can’t tell which way up they are by feel. You are told that there are 5 coins head up, and ...
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2answers
179 views

A question of.. Probability! [closed]

You have six loaded dice (I mean falsified, non regular). In the first die there is always a $10\%$ of probability for $1$ to come out. In the second die there is always a $20\%$ of probability for $...
3
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1answer
181 views

Gambling with the gambler [closed]

You are walking on the street and notice a guy gambling with some other guys and you start to watch. The game principle is pretty easy. There is a standard 52-card deck and it is being shuffled every ...
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2answers
369 views

The most probable key

You broke into John Doe's house and found the safe. It has a combination lock with 4 dials ranging from 0 to 9 each. ...
3
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2answers
148 views

Check-out counter at a supermarket [closed]

A check-out counter at a supermarket will service one customer per unit time if there is anyone in line. Customers arrive at the line: in each unit of time, the probability that a single new customer ...
3
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2answers
317 views

Return to the Minotaur's Labyrinth

This is an extension of the puzzle The Minotaur's Labyrinth which is inspired by the comments from histocrat. You are trapped (again) in a chamber at the center of the minotaur's labyrinth. There are ...
3
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2answers
2k views

A modified version of apples and oranges logic

Question: You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. ...
3
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1answer
178 views

A Chuck-a-luck variant

You're thinking of trying a variant of Chuck-a-luck. In this variant, you choose one number in the range $1$ to $6$ and five dice are rolled. These are the payouts: ...
3
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2answers
210 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 ...
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0answers
110 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 ...
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0answers
47 views

Knight's Tour Question [duplicate]

A chessboard is an 8 × 8 grid. A knight can move up two squares plus one square to the left or right, or up one plus two squares to the left or right. For a knight in the position shown, determine the ...
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3answers
2k views

Should I take the antidote? [closed]

A new disease has been discovered in the world, it is called Blue. Statistically 1:1000 people in the world has it and it makes your whole skin blue in a few weeks after getting the disease but not ...
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3answers
400 views

A game with numbers [closed]

Two people randomly select two different 1-digit numbers (including 0 of course) and calculate their absolute difference. Then They share what they get, What is the probability of having the same ...
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2answers
352 views

How to beat Count Dracula, part 2

This is a follow-up to "How to beat Count Dracula". Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. The three players agree on the following rules: Count Dracula and ...
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4answers
1k views

4 player card game, who has advantage? [closed]

Edit for "off topic" "correction". I don't know why this question was considered "off topic". It seemed to draw a lot of attention. The "puzzle" was to figure out which person has the advantage ...
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2answers
1k views

How many keys will we try before opening the door? [closed]

You have N keys, exactly K of which will open your door. If you tries keys at random and you never try the same key twice, then X is the number of keys you will try before opening the door. X is a ...
2
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1answer
141 views

Sleeping Beauty Study at the Institute of Mad Science [closed]

You've been approached to assist in the furtherance of SCIENCE as a research subject at the Institute of Mad Science (local branch)! The experiment you'll be involved with is called the Sleeping ...
2
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1answer
120 views

Can you build a Rubik's Cube? [Part 2]

You are given an disassembled Rubik's cube (Detachable centers,corners and edges). You are then blindfolded. If you assemble the cube while being blindfolded. What is the probability that the cube you ...
2
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2answers
309 views

A Shooting Target with 9 shots

You are a soldier in the army, and the commander is testing his soldiers for their shots. But the commander is also a mathematician and would like to test not only your shooting ability but also your ...
2
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1answer
160 views

Dice problem involving nine randomly selected cups [closed]

I was given this problem by a colleague, and I cannot figure it out. Given nine cups and an unlimited supply of six-sided dice rolled one at a time, what is the probability that you will, at some ...
2
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2answers
152 views

Halve or diminish, and race to unity! v2

This is follow-up question to Halve or diminish, and race to unity!. Alice and Bob are playing a game. In the beginning, they randomly choose a positive integer between $2$ to $n$ where $n$ is a ...
2
votes
1answer
1k views

Climb the ladder [closed]

You are above a pit of fire and the only way out is a $1000-$ rung escape ladder. You're on the first rung. Every second a standard die rolls. If it's $1$ or $2$ you move down one rung. Otherwise you ...
2
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3answers
562 views

What is the value of this other coin flipping game?

This is variation of this question: What is the value of this coin flipping game? Imagine that you can play the game in a casino - you are flipping a fair coin. If you get tails, the game continues ...
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2answers
92 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 ...
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2answers
850 views

100 sequential parking spaces

I just came up across this question in the mathematics stack exchange site and found it quite interesting: 100 autonomous robotic vehicles enter a warehouse in random order to park. Inside the ...
2
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1answer
256 views

2 aliens walk on a line meeting probability [closed]

2 aliens walk on a line randomly. At each timestep they walk independently either left or right (1 meter) with equal probability. They start 10 meters apart. What's the probability that after 7 time ...
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2answers
250 views

N strings in a bag

There are n strings in a bag. In one pass, you randomly pick one end of a string and then one more string. Then you tie these two ends together and put the resulting string back into the bag. Then ...
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0answers
181 views

German Tank Problem [closed]

"Alright," says the commander gruffly. I try not to stare at the biscuits in his beard. "This week we've captured 5 German VX-Tanks, with serial numbers numbers 3, 5, 13, 22, and 27. They stopped ...
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4answers
2k views

100 chocolate bars! [duplicate]

A boy was taken to a magical land of wonder and chocolate, but sadly, a disease broke out in this land! He has to face off the evil Dr. Vanscosh, who caused the disease to break out, in a probability ...
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4answers
2k 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 ...
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2answers
442 views

The Trump Brotherhood

If you happen to meet two of the Trump brothers from the family that lives down the street from you (assume that the two are random selections all of the Trump brothers), it is an even-money bet that ...
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5answers
778 views

Another look at the two children riddle

Inspired by this question about the Monty Hall problem, here's a deeper look at another well-known counter-intuitive probability problem which is often stated in a way that leaves subtle ambiguities: ...
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3answers
156 views

What are the odds that everyone has a partner at a club? [closed]

I badly misread this problem: You just won 2016 socks. Some of them are white, some are blue. The color of each sock was randomly chosen, with a 50/50 probability. Is it more probable that the ...
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3answers
206 views

Jack and Jill went up the Hill to play

A Simple Card Game. This deck of cards has only four cards simply labeled 1, 2, 3, 4. They are placed face down. Jack and Jill take turns to draw a card. You sum up the numbers drawn so far after ...
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2answers
544 views

Roulette tournament?

You have been invited to play in a French Roulette tournament. The tournament-specific rules are as follows: You start with 100 tokens Play lasts for 5 rounds Minimum bets based on color, low/high (1-...
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2answers
235 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 ...
1
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1answer
357 views

Probability in chess tournament

In a 4 round chess tournament with 16 players (where the loser of each two player match is eliminated and the winner moves on to the next round), the pairings for all matches are decided randomly. The ...
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1answer
52 views

Place Your Bets 2 - In sequence, of course

Your Cards... You have to figure out what the next row of 4 cards will be. There is a pattern in there somewhere, promise. Good Luck
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1answer
83 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 ...
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1answer
105 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 ...
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2answers
164 views

Landing 4 on a Broken Die [closed]

This is not hard, but fun. Suppose you have a die such that its 1,5,6 and 4 face are broken. Whenever 1 face lands, it gets rolled over to an adjacent face. If 5 face lands, it is equally likely that ...
1
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1answer
157 views

Simple probability game [closed]

You are asked to play a classic shell game with two shells. Each round, a ball is placed under one shell, the shells are rapidly, continuously rearranged for 15 seconds with distraction*, and then ...
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1answer
74 views

Chess Puzzle to calculate the minimum number of movements of pawn [closed]

Given an N×N chessboard, with two pieces, a black pawn and a white pawn randomly placed on the chessboard. What is the minimum number of steps required by the white pawn to reach the black pawn under ...
1
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1answer
168 views

Another Unconventional Dice Blackjack game - is Nash equilibrium here?

This question is similar to This Dice Blackjack game - is there Nash equilibrium?, but the game rules are completely different. This Dice Blackjack is game for two. It is also played with fair six-...
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1answer
285 views

Eight Suspects and a Crazy Executioner

A group of 8 suspects; 3 wearing red shirts, 2 wearing green shirts and 3 wearing blue shirts. Eye-witness claims to have seen 3 people in the scene, the shirt of one of them appeared red, while the ...
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2answers
148 views

Finding a random number in a randomly assigned number in boxes [duplicate]

In a closed room, paper slips labelled $1$ to $100$ are randomly put into boxes also labeled $1$ to $100$. You win a big prize if you can locate a given number (from $1$ to $100$) by opening no more ...
1
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2answers
179 views

Fumbling with a question already posted

This question, has me stumped. Looking at the first version, how there's two lines of thought that go around in my head, both (seemingly) justifiable. 1 : 'One of them is a girl' implies 'Both ...
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0answers
88 views

Find the probability [on hold]

There are n number of people in a room. If any two people doesn’t know each other, they shake hand. At the end, ever body announces their number of hand shake. Total number of handshake is : N(N-1)/2 ...
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2answers
223 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 ...
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0answers
127 views

Tic Tac Toe and random turn puzzle [closed]

I have a problem: There is a bag of 75 balls with 15 Red and rest Blue. I pick 4 balls at the start of every turn.If I get to pick at least 1 red ball, I fill 1 cell with X. If I get 3 red balls ...