We’re rewarding the question askers & reputations are being recalculated! Read more.

Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

Filter by
Sorted by
Tagged with
1
vote
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 ...
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
119 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 ...
0
votes
2answers
678 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
459 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 ...
7
votes
3answers
530 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 possible), but it ...
4
votes
2answers
562 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
652 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
177 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 ...
21
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
290 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
48 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
votes
2answers
153 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
210 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
619 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
818 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
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 ...
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
435 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
722 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
542 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
275 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
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 ...
0
votes
2answers
227 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
136 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
728 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
158 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
334 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
605 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
390 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 ...
8
votes
2answers
314 views

Expected value of a milion dollar (equal?) division

I've heard this riddle a while ago and it is quite interesting. Say I've got two sons and one million dollars to spare. Each boy gets one dollar as a start and from there I give them dollar by dollar ...
-4
votes
1answer
201 views

A taxi was involved in a hit-and-run accident last night [closed]

A taxi was involved in a hit-and-run accident at night. Two taxi companies, the green and the blue, operate in the city. 85% percent of the taxis are green and 15% are blue. A witness identified the ...
9
votes
2answers
418 views

How to beat Count Dracula, part 3

This is a follow-up to "How to beat Count Dracula" and to "How to beat Count Dracula, part 2". Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. The three players agree on ...
2
votes
2answers
353 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 ...
10
votes
8answers
1k views

A Lazy Way to Make Two Dice from Many

Recently, I stumbled upon the puzzle: Make Two Dice out of Three, which asks for a solution to a case of the following question: Suppose I roll $n$ indistinguishable dice. From purely the $n$ ...
1
vote
1answer
288 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 ...
11
votes
1answer
3k views

Deceptive dice game

You must create a set of 6-sided dice and play a game with an opponent. The dice are like regular dice, but you can change the numbers on the dice. For example, regular dice have sides ...
1
vote
2answers
547 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-...
15
votes
3answers
2k views

A way to beat the system?

I and my friend have always had an interest in gambling. Every week, we each have $£100$ to spare, and we like to bet it on football games at the bookmaker’s. In the long term, we (unsurprisingly) don’...
26
votes
10answers
3k views

Make 2 dice out of 3 dice

This question was first posted by standupmaths on youtube: https://www.youtube.com/watch?v=xHh0ui5mi_E He already got some answers but I think this community can probably find a better answer. ...
8
votes
2answers
406 views

Kangaroo on a square

A kangaroo is jumping around on the corners of the square ABCD. The kangaroo starts at corner A. In each jump it moves to one of the two adjacent corners, with a probability of exactly 1/2 for each. ...
8
votes
7answers
2k views

Mr. Gardner's dessert

Mr. Gardner is facing the choice of dessert at his favorite restaurant The Erratic Chef. The cook tends to prepare great desserts, but is not very consistent. Mr. Gardner hates it when his choice for ...
6
votes
2answers
310 views

More coin flipping

After their last game, Alice and Bob decide to have a bit more fun with their fair coin. Bob proposes the following game: considering a flip can come out as heads or tails, they will both predict one ...
8
votes
2answers
496 views

The asymmetric coin game

After finding a coin in her farm, Alice proposes the following game to Bob: Alice will flip the coin $n$ times. Bob will then flip the coin $2n$ times. If Bob manages to get the same amount of ...
35
votes
1answer
5k views

Say 100 and win

Our good friends that like games, Alice and Bob, play a game called "Say 100 and win". The rules are: In the beginning they use one regular 6 faced die to get a random number between 1 and 6. Let's ...
7
votes
1answer
248 views

Coin with two heads [closed]

I was at a job interview and got a question. You have a bag with 100 coins. One of these coins has two heads, other coins are regular. You get one coin from this bag, put it on a table and see head. ...
14
votes
5answers
2k views

The Good, the Bad and the Ugly

Tuco, Blondie and Sentenza play a game with a single die. Tuco has the first roll, then Blondie, and then Sentenza, and so on. As soon as a player tosses a six, that player drops out of the game and ...
13
votes
6answers
1k views

A set of lockers

There is a series of 100 lockers in a school. All of them start closed. Students number 1 to 100 flip an even, two sided coin. If the coin lands on heads, they go through each locker corresponding ...