Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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6
votes
2answers
733 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
551 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
296 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
234 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
159 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
734 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
162 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
337 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
613 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
405 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
317 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 ...
-5
votes
1answer
212 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
433 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
364 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
306 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
582 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
408 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
315 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
513 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 ...
36
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 ...
14
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 ...
7
votes
3answers
2k views

No two heads in a row

Suppose I toss a fair coin a 100 times. What is the probability of not getting two heads in a row?
10
votes
5answers
2k views

Unfair coins at South Park Elementary v2

Following Unfair coins at South Park Elementary Wendy and Sally have another friend, called Timmy. Although Timmy has no coin, he wants to play this game in a fair condition with them. Wendy does the ...
15
votes
8answers
5k views

Unfair coins at South Park Elementary

Wendy Testaburger and Sally Turner play a game with two unfair coins. A coin flip with Wendy's coin shows head with probability $\frac {1} {100}$. A coin flip with Sally's coin shows head with ...
5
votes
3answers
1k views

Domino tile possibilities

I own a normal domino game with 28 tiles. Each tile carries two of the numbers [0, 1, 2, 3, 4, 5, 6] (where 0 represents blank). During cleanup five pieces fell out of the box. Two of them showed ...
13
votes
5answers
891 views

Seven cowboys play a coin tossing game [closed]

Seven cowboys play a coin tossing game with a fair coin where each player has a chance of 1/2 of winning. Each of them plays once against all other six. What is the probability that each cowboy wins ...
11
votes
3answers
1k views

Seven cards in a bowler hat

The game show host puts seven cards with the numbers 1, 2, 4, 8, 16, 32, 64 into a bowler hat. The candidate picks cards up randomly from the hat, one card at a time, and without putting cards back, ...
6
votes
5answers
3k 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 ...
15
votes
5answers
1k views

The Price is Right [closed]

A real life puzzle, yesterday on The Price is Right a contestant played the following game: She could choose 5 cards from a pile where 2 cards were "Car", 11 were "C", 11 were "A" and 11 were "R". ...
6
votes
1answer
410 views

Corollary to “A game with 52 cards”

Inspired by A game with 52 cards Alice and Bob play the following game with two (identical) standard decks of $52$ cards. First Alice secretly arranges one deck of $52$ cards in a long row ...
-1
votes
2answers
173 views

A chance to know 52 cards [closed]

This is the Follow up Question to A game with 52 cards. So it requires to understand previous question! I believe it is a bit harder to find! what is the chance to know the positions of all the face-...
41
votes
1answer
3k views

Crippled King Crossing a Canyon

A chess king has been injured in battle against an evil wizard, and can no longer move northeast or southwest. This king is on the North rim of a canyon, and must flee to safety on the South rim. ...
5
votes
0answers
152 views

Finding the numbers [duplicate]

I found a nice problem. Here is what it says: Kevin and Peter are given a piece of paper each where they write a number. Their friend John comes up and takes the two pieces of paper and opens them up ...
2
votes
3answers
405 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 ...
2
votes
3answers
570 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 ...
12
votes
3answers
1k views

Three Cafes Puzzle

Every morning a couple has breakfast at one of three cafes: Amy's, Bob's, or Cindy's. After eating at Amy's or Bob's, they flip a coin to see which of the other two cafes they'll go to the next ...
7
votes
1answer
164 views

The Attack on Fort Alpha

I made this puzzle up in 1999 when I was a student. Fort Alpha, on your border territories, was attacked by The Enemy. You don't know if it fell, or repulsed The Enemy's vicious onslaught. A totally ...
16
votes
6answers
5k views

99 doors to death!

You wake up in a small locked room of a huge castle. There are 100 doors, numbers 1 to 100, and you are to open one of them. Open the correct door, and the entire castle is yours to keep. Open any of ...
3
votes
2answers
2k views

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 ...
43
votes
3answers
3k views

Relabeling two 20-sided dice without changing their total

Usually, 20-sided dice are labeled with the numbers 1 to 20. When you roll two of these, their sum is a random number between 2 and 40. The total 21 is most likely to occur, while 2 and 40 are the ...
4
votes
2answers
346 views

Card Passing Game

13 friends are sitting around a table. They shuffle a half-deck of cards, consisting of only the black cards of a standard deck, and deal out two cards to each person. There are then a series of ...

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