The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

Filter by
Sorted by
Tagged with
13
votes
5answers
889 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
397 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
171 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
147 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 ...
2
votes
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 ...
2
votes
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 ...
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
162 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
4k 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
1k 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
334 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 ...
3
votes
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 ...
1
vote
2answers
150 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 ...
6
votes
4answers
380 views

Drawing uniformly using a single biased coin

Your task is to draw uniformly from a set of size $N$. You are given a single coin which you can ‘bend’ to control the probability $p\in[0,1]$ of throwing a Head, but you are only allowed a bounded ...
17
votes
1answer
601 views

Two Dice = Nine Cards

I have nine cards, each labeled with a real number (possibly negative or fractional) in a special way. When I randomly pick two of these cards without replacement and add their labels together, the ...
4
votes
3answers
1k views

In a Guess The Color game, what's the optimal strategy?

Here's a one-player card game: We begin with a shuffled card deck The player try to guess the color of the card at the top (black or red) If the player guess right, he can keep the card. Else the ...
9
votes
4answers
681 views

Nerves of Steel (a dice game)

A carnival offers a game, called Nerves of Steel. It is played with a standard die, except that the "six" has been replaced with a skull. You start by paying $7, then rolling the die. Each time you ...
7
votes
3answers
1k views

Surviving Captain Nefarious

Captain Nefarious has captured you and two of your friends, Alice and Bob. Being a villain, he has a natural desire to monologue, so he sits you down (guarded, of course by his Largely Incompetent ...
5
votes
1answer
542 views

The Minotaur's Labyrinth

You are trapped in a chamber in the center of the Minotaur's Labyrinth. There are $\mathbf{N}$ tunnels, $\mathbf{m}$ of which lead to safety; the remaining tunnels only lead back to the chamber. Each ...
39
votes
22answers
8k views

Aproximating 100 by 6

You're a fan of pen & paper RPGs and have finally arranged a new playing group, recruited amongst your friends from the mathematical faculty. As a GameMaster (GM) you've assumed that all your ...
3
votes
2answers
180 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 $...
4
votes
2answers
1k views

A coin flip's long tail

I have a (possibly-) unfair coin, which lands heads with probability $p$ and lands tails with probability $1-p$. I toss it twice; the tosses are independent and identically distributed. The ...
28
votes
3answers
4k views

A lonely pawn on the chessboard

Alice and Bob and the referee Conny play the following game with a pawn on a standard $8\times8$ chessboard: In the beginning, Conny places the pawn into the center of a randomly chosen square. All $...
6
votes
2answers
580 views

A jar of mixed coins [closed]

This is a slight adaptation of a google interview question that I found entertaining. You are given a jar with N coins, K of them are fair. The remaining coins have heads on both sides. You choose a ...
12
votes
4answers
783 views

Asimov's Robot Balloon Trip

Chuck Asimov is a keen inventor and balloonist. He has developed some humanoid robots and decided to take nine of them (conveniently numbered 1 to 9) on a trip in his hot air balloon. Unfortunately ...
6
votes
3answers
351 views

Intersecting bug trail [closed]

A man picks up a huge circular dart board and shoots paintballs at it. $n$ paintballs manage to hit it. They are random and point-sized, for the purpose of this question. A bug is somewhere on the ...
3
votes
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: ...
17
votes
6answers
5k views

What is the expected value of this coin flipping game?

A casino offers the following game: You flip a fair coin repeatedly and record the results on slips of paper, one result per slip. At any time you may decide to stop, at which time one of the slips ...
-1
votes
2answers
275 views

Kill for a young body [closed]

FROM 2013 Real Playing Game. Here's the trailer. You are an old, deathly-ill multimillionaire. A biotech company has developed some brain transfer technology and offers you the chance to ...
7
votes
4answers
756 views

Born to lie, to live, to die

There is a race which has a truth gene. It consists of 3 alleles, namely T, F and O. A person inherits one allele from each of his parents, hence he/she has always exactly two alleles. For example, if ...
2
votes
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 ...
19
votes
3answers
1k views

Shooting Free Throws

Shaq is shooting free throws. He makes his first shot, then misses his second. Confidence is a huge factor in how well Shaq plays. This means that for each subsequent shot, the probability he makes ...
2
votes
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 ...
14
votes
7answers
2k views

Poker and a card shark

I am playing poker with three friends and from a well-shuffled deck we have each been dealt five cards. I have a hand consisting of the four kings and the two of hearts. Being a poker wizard I know ...
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:" ...
6
votes
2answers
752 views

The Fanatic Fever(twist on the 5 pirates puzzle)

While raiding a tropical island, 6 pirates have an incredibly unlucky day. While they scoured the island in search of treasure, one of them was infected with the Fanatic Fever, a disease which hits ...
13
votes
3answers
666 views

100 Dwarves vs. the Evil Elf

The following is an extension of 100 Dwarves and a tiny room. The text of this puzzles spoils that one in a minor way, so go read that excellent puzzle first! An evil elf puts $100$ dwarves in a ...
14
votes
2answers
1k views

Crazy Dice - Unusual Dice with Usual Sum

Can you design two six-sided dice (different from the standard ones), where each face has a nonzero number of dots, so that the probability distribution of their total is the same as for two standard ...
15
votes
7answers
3k views

Loaded Dice with Uniform Sum

A loaded die looks like a regular six-sided die, but instead of each number 1-6 being equally likely, some numbers may be more or less likely than others. Is it possible to have two loaded dice so ...
9
votes
3answers
2k views

How to cheat at cards

I have a deck of 52 cards on the table in front of me, in random order, each one randomly facing either up or down. I place one joker at each end, each of these again randomly facing either up or down,...
11
votes
5answers
484 views

One Hundred Lockboxes, Variant

You have one hundred lockboxes, fifty made of steel, fifty made of wood, and a key for each box. A prankster breaks into your house and distributes the keys among the boxes. He places each key in a ...
20
votes
2answers
2k views

One Hundred Lockboxes of Wood and Steel

A bit beyond perceptions reach, I sometimes believe I see that life is two locked boxes, each containing the other’s key. ― Piet Hein You have one hundred lockboxes, fifty made of steel, ...
17
votes
1answer
1k views

Contagious ants on a stick

Twenty-five ants are scattered on a meter stick. At the same time, they each pick a random direction (east or west) and start marching at 1cm/second. Whenever two ants meet, they turn around. When an ...
0
votes
2answers
1k views

question involving two deck of cards [closed]

Consider two identical card packs: A and B. One card is taken from A and shuffled with pack B. The top card of pack A is QUEEN of HEARTS. What is the probability that the top card of pack B is KING of ...
14
votes
13answers
5k views

How to get a uniform 1 out of 7 chance, using only a coin and a 6-sided die

There are seven days in a week. Let's say you want to pick one at random, such that each day has an equal chance of being picked as each other day. In other words, the goal is to obtain a uniform ...