Questions tagged [probability]

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

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4
votes
3answers
628 views

Effective strategy for prisoners to see movie

100 prisoners are given an opportunity to go to a theatre and watch a movie. Each can choose either to go or not. However, if everyone chooses to go to the trip then no one is allowed to go. The ...
9
votes
4answers
466 views

Number exchange game

Inigo and Vizzini are to have a battle of wits to the death. The rules are: Inigo is given two independent random numbers uniformly distributed between 0 and 1. Inigo chooses one of the numbers to ...
4
votes
3answers
713 views

What are the odds for the student to be right? [duplicate]

If a student answers this questions randomly, without thinking, what are the odds he will get the question right ? 25% chances 1 in 2 chances 75% chances 1 in 4 chances EDIT : This question is not ...
14
votes
2answers
5k views

How to simulate one die with three dice?

I do not know if there is a correct solution to this puzzle, but I can't stop thinking about it, so here goes: is it possible to accurately simulate a single, fair, six-sided die using three custom ...
1
vote
1answer
221 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-...
1
vote
3answers
530 views

This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
1
vote
1answer
164 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 ...
1
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2answers
453 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 ...
2
votes
1answer
132 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 ...
6
votes
1answer
1k views

cheating on the Russian roulette

This question is inspired by this one. You and your opponent play Russian roulette with two bullets. Quoting from the linked question: You are challenged to a game of Russian roulette. Your ...
5
votes
2answers
857 views

probability tricky question

Nils has a telephone number with eight different digits. He has made 28 cards with statements of the type “The digit a occurs earlier than the digit b in my telephone number” – one for each pair of ...
2
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0answers
201 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 ...
3
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2answers
372 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 ...
7
votes
2answers
616 views

Twin Probabilities Problem

1 in 8 sets of twins are sets of identical twins. While talking to Jessica, you learn that she has a twin named Emily. What's the probability that Emily and Jessica are identical twins? The answer ...
-6
votes
5answers
153 views

Underpants in a Drawer [closed]

I have 22 underpants in the drawer and it is dark and I cannot identify the colors. 3 pairs are red. What is the probability of my putting on a red pair of underpants from the drawer? 3/22 is the ...
2
votes
1answer
261 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 ...
5
votes
5answers
486 views

Russian roulette

You are challenged to a game of Russian roulette. Your opponent places two bullets side by side in a six chamber revolver and spins the chamber. She explains that the game is single turn-based and ...
-6
votes
1answer
280 views

The Puzzling Phone [closed]

The amazing "Puzzling Phone", comes in two models, one sold by "Super Puzzling Inc", and one sold by "Mega Puzzling Ltd" Phones need to have government testing before they can be sold on the market. ...
1
vote
0answers
141 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 ...
0
votes
1answer
1k views

100 coins (Heads and Tails) [duplicate]

"You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can't feel, see or in any other way find out which side is up. ...
-4
votes
3answers
143 views

What is the probability that no one will get his envelope? [closed]

You are given 100 addressed envelopes and 100 addressed letters to be inserted into the envelopes. If the letters are inserted randomly into the envelopes, what is the probability that no letter will ...
1
vote
2answers
849 views

Open doors brain teaser [closed]

There are three doors before you, of which only one is correct. Each door will take you one minute to open by default, but one of the incorrect doors contains a trap that will slow opening of any ...
3
votes
5answers
479 views

Why is my car always in the slowest lane?

Staying in the traffic again this morning, I decided to find a mathematical motivation behind me always being in the slowest lane. Consider the following formalization: there are 4 empty lanes and ...
8
votes
3answers
717 views

Building the ideal Scrabble dice set

This is a genuine question and I don't know the "correct" answer to this. I'm also of two minds if it is really on-topic on the site. Finding the answer is surely "a puzzle" (if ...
4
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2answers
627 views

The Monty Hall Arena

Monty Hall had enough of all these pesky mathematicians winning cars. Quite demotivated, he modified his show: There is a finite number $n$ of doors There is one car behind a door, otherwise there ...
7
votes
1answer
665 views

Will You (Yes, You) Decide The Election? [closed]

You are the only sane voter in a state with two candidates running for Senate. There are N other people in the state, and each of them votes completely randomly! Those voters all act independently and ...
-4
votes
1answer
179 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, ...
11
votes
3answers
1k views

A hat puzzle involving wizards

Two wizards, Alice and Bob, each have two hats on their heads. Each hat is independently black or white with probability one-half. When the game starts each wizard will see the hats on the other ...
22
votes
1answer
1k views

Monte Carlo Chess

This is an entry to the 17th fortnightly topic challenge. Chess is an interesting game, but is so unrealistic. In real life, you couldn't tell order your knight to attack an enemy bishop and expect ...
-5
votes
2answers
295 views

The four prisoners [closed]

Four prisoners, 1, 2, 3 and 4, are all condemned to death. One of them is at random selected to be pardoned. 1 asks the guard who will be executed. The guard refuses to tell him so instead 1 says '...
3
votes
0answers
55 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 ...
2
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2answers
169 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 ...
-5
votes
1answer
214 views

Black socks and green socks [closed]

Some green socks, some black socks, their total is four. Some green socks, some black socks, some socks on the floor. The chance of getting two black ones, the chance of getting two black ones, that ...
-3
votes
9answers
638 views

5 guards, 5 doors, and probability

1st Guard: Always lies all the time. 2nd Guard: Always tells the truth all the time. 3rd Guard: 75% probability of telling the truth. 4th Guard: 50% probability of telling the truth. 5th Guard: 25%...
4
votes
6answers
947 views

Best strategy to get all heads/tails from three coins

Your friend has 3 fair coins: a dime, a nickel, and a quarter. She places them on a table behind you. She can arrange then in any pattern of heads and tails as long as they are not all the same. You ...
3
votes
2answers
153 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 ...
8
votes
7answers
1k views

7 Numbered Balls Game

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 are 7 balls in a pouch and you have 3 balls to draw ...
7
votes
3answers
469 views

Two Dragons and a Princess

The Quest You are a knight tasked with rescuing the King's daughter. The princess is being held captive by a band of evil dragon pirate monks. You've been debriefed with prior intelligence gathered ...
6
votes
2answers
742 views

A book with only two letters

Dr. G somehow detests reading novels but he decided to read a one then he naturally got bored and decided to delete all letters except A and B letters in the book. So with this new book which ...
4
votes
3answers
576 views

Dr. G's Interesting Theorem on Playing Cards

Dr. G has spent his last weekend with analyzing $n$ number of cards which are numbered from $1$ to $n$. He has a fair shuffling machine for his cards and while playing and drawing some cards, he uses ...
4
votes
2answers
331 views

Optimal solution to a modified poker game

Note: Knowledge of the poker game Texas Hold-em is (probably) needed in order to answer this question. You and a friend (only two people are playing) are playing a standard game of Texas Hold-em but ...
10
votes
5answers
1k views

Who will win this dice game? [closed]

You are playing a dice game with your friend by rolling two standard dice and recording the sum of the two numbers. You win when two consecutive outcomes are 7. Your friend wins when three consecutive ...
2
votes
1answer
2k 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 ...
0
votes
2answers
236 views

Darts on a dartboard [closed]

I have $x$ darts that I randomly throw on a dartboard with $y$ slots (the v shaped slices like you get when you cut a cake). Now I select a particular slice on the dartboard . What's the probability ...
0
votes
2answers
183 views

Solitaire wins and losses

Let say a solitaire game can be solved 1 in 10 plays. (A play is defined as shuffling of cards and trying to solve the solitaire). If after each successfully solved game we skip 8 games (we ...
7
votes
2answers
758 views

What are the chances you lost a nickel?

Yesterday you had 50 coins totaling exactly one US dollar in value. Somehow you lost one of those fifty coins on the way to the vending machine. Assume the likelihood of losing each coin (regardless ...
1
vote
3answers
165 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 ...
7
votes
2answers
347 views

Where the water is hotter

There are two perfectly identical boilers containing the same amount of water, switched on and working in identical environments. Both are setup so that the heating starts when the temperature of ...
14
votes
5answers
623 views

Socks which may or may not match

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 socks can be paired, or that you will ...
10
votes
2answers
432 views

A cell in an infinite culture

A single-celled organism is placed into an infinite culture. This cell has the genetic property that it has a $p = 3/4$ chance of splitting into two cells before it dies, and all its children will ...

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