Questions tagged [probability]

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

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7answers
1k views

Prisoners and minority voting

Disclaimer: this is a scenario that I came up with on my own, and I do not actually know if there is a possible solution. The reason for posting is to see if the combined intellect of PSE can help to ...
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2answers
431 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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1answer
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Lost first game – can I still make my mother proud?

I am one of the greatest finger wrestlers of my generation. Only 0.1% of all players are better. When I play against someone who's worse than me, I win 99% of the time. Against someone who's ...
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2answers
2k views

Two Card Probability Problem

I came across this puzzle somewhere on the interwebs. Has stumped me for an answer for quite sometime. Helpplease? Someone picks, at their will, two cards from a deck of cards. The cards have ...
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3answers
875 views

Five pirates splitting gold with a twist

Source: This was posted on the Grey Labyrinth Forums many years ago. The five pirates are back. But this time one of them has the dreaded Zanzibar fever, whose terrible effects are spelled out below....
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1answer
521 views

Mathematics in adolescence

When I start to teach probabilities, I challenge my students with the following: Thelma is 16 years old and can only go out at night if one of her parents gives her permission. She knows her father ...
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4answers
721 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 ...
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1answer
542 views

Expected number of squares in a 20x10 grid with 1% chance of removing each edge

Suppose I make a 20x10 grid out of match sticks, using 21 columns of 10 match sticks and 11 rows of 20 match sticks: ...
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3answers
338 views

Find a good strategy to survive the multiplayer duel

Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can ...
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1answer
341 views

Birthday girl's casino game

My daughter's birthday is coming up. Here's a fun party game we can play to celebrate. (Bring your wallet!) I have a pair of 6-sided dice, and a standard deck of 52 cards. You place your ...
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4answers
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Rocks and Lever (Game) - Goofspiel

I am not sure if there is a name associated with this game but I do not know of one. There was this 2 player game I had once played, and I am wondering if there is a winning strategy. The game is as ...
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2answers
476 views

How should you distribute the fighting power?

Alice and Bob both have N warriors under their command, numbered 1~N, and $1$ point of fighting power at their disposal. Before the game, they privately distribute the power between their warriors. ...
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8answers
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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 $n$ ...
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2answers
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Entangled physicists

The anti-intellectuals have won the war, and under the iron rule of emperor Nonotin anyone who has been deemed too smart for their own good has been brought to labour camps. But most of the science ...
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9answers
3k views

How many gold coins can you extract from the billionaire?

An eccentric billionaire plays a game with you. She has an urn with 100 gold coins. Each time, you can take any number of coins from the urn. If you take n coins, she will flip a fair coin. If head, ...
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3answers
4k views

Is my sibling a sister [duplicate]

A male friend of yours wants to test if you are ok at Math and logical thinking, he says I am one of two children of my parents, and asks you to find out the probability that his sibling is a sister, ...
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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,...
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5answers
436 views

The Two Envelope Game Show

This is an original riddle I made, heavily inspired by the Two Envelope problem. I have my answer to this problem, but (full disclosure) even I’m not 100% sure I’ve got it right. I post it half ...
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5answers
1k views

How long will my money last at roulette?

I'm at the casino, standing next to a roulette table with a \$10 minimum bet. I want to stay here as long as possible, so I'm going to repeatedly make the minimum bet until I run out of money. I'm ...
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2answers
454 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 ...
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3answers
460 views

A box full of unfair coins

Lolek and Bolek are arguing on whose turn is to take out the trash. They have a box with $n$ coins. when the coin $i$ is thrown, the probability that it lands on heads is $p_i$. They decided to make ...
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4answers
462 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 ...
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3answers
1k views

A first choice die

You and your friend have met to play a game of dice. This is a very simple game where both players roll a die at the same time, and the player with the lower score pays a coin to the other player. In ...
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5answers
379 views

Find the optimal strategy for this dice game

You are playing a game: You have $6$ standard 6-sided dice that are all rolled at the start of the game. The sum of dice values is your score. Each turn, you can take any (or none) dice and reroll ...
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3answers
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Sliding Bolt Puzzle - fastest solution (time-wise)

This is a follow-up question for the Sliding Bolt Puzzle. If you have not solved it yet, you might want to head there first, as the extended discussion of its solution in this question will contain ...
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2answers
399 views

Three way duel, which guns to choose?

Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
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2answers
690 views

What is the probability that all the bullets will be destroyed?

A gun shots bullets with different speed each second. The bullets form a straight line. The bullets keep their speed (not getting slower or faster). But if 2 of the bullets collide, 2 of them are ...
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3answers
684 views

Generalizing the “shooting puzzle”

Inspired by this puzzle. You have $n$ shooters having a duel, labeled $1, 2, ... n$. Each shooter has an accuracy of $k_n$, with each $k_n$ some probability in $(0,1]$, with $k_1 < k_2 < ... &...
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2answers
222 views

What are the odds that there is no solution on a given Set board?

I was playing a game of Set with a group. We had the usual twelve cards out and all agreed that there was no set. We then increased the number of cards to fifteen and were still unable to find a set....
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6answers
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100 pieces 1 opportunity, choose wisely!

Say you have a cake that is cut into 100 pieces. One of the pieces has a hidden prize. 100 people take turns, each taking a piece in sequence hoping to find the prize. Note: I slightly modified (...
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7answers
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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 ...
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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 ...
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2answers
415 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. ...
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2answers
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Keypad Door Lock

Your progress is barred by a locked door, it is clearly controlled by a keypad. with 10 digits (0-9) plus a button for ENTER and a button for CANCEL. You know several things about this lock: This ...
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4answers
998 views

Social Engineering (The Birthrate Problem)

The distant country of Toomalia has a birthrate of 67 boys for every 33 girls. In an effort to restore a 50:50 gender ratio in the country, Toomalian policymakers institute a mandatory new social ...
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2answers
860 views

Wait, it is worth it?

You went to a Casino, and saw a quite interesting stall. The cardboard besides the stall says: You first pay \$$5$ You have to toss the fair coin. If it lands heads, you can ...
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2answers
543 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 ...
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3answers
704 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 ...
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1answer
273 views

Mission: Impossible 2

Ethan Hunt is tied to a chair and can't get up. The super-villain Matt Fillimore stands in front of him. There's a gun. There's the barrel of the gun, six chambers, all empty. Fillimore is putting two ...
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3answers
853 views

The tile-flipping game

The tile-flipping game uses 6 tiles that have a white side and a black side. It starts with the tiles arranged in a line with their white side facing up. $$\circ \circ \circ \circ \circ \circ$$ We ...
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4answers
625 views

Circle inside circle

Here's a fun little math problem I made(by fun I mean no complicated methods needed at all.) You have a large circle with radius N with a cross in it to seperate the 4 quadrants(so that the figure ...
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1answer
328 views

Frog in the Well [duplicate]

A frog is trapped in a well, just 1 meter below the lip. On sunny days, the well is dry, and the frog is able to climb up 1 meter. On rainy days, the well is wet and the frog slides down 1 meter. If ...
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5answers
860 views

Two person game, choosing an integer between 1 and 30?

Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
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2answers
620 views

Help! I lost my marble(s)!

Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The days festivities will include various marble games, admiring collections of marbles, a guest speaker who will talk ...
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1answer
129 views

Black-hat/white-hat logicians with a bell and a meal

At the 2020 yearly black- and white- hatted logician gathering, the following fun activity is organized. $N$ logicians will sit around a table, each wearing a black or a white hat the color of which ...
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5answers
548 views

Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
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2answers
324 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 ...
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8answers
626 views

Five Haberdashers

This is yet another hat puzzle, but not one of the usual ones! Key differences/commonalities between other hat puzzles are emphasized. Five friends are going to go on a game show. When the game ...
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1answer
277 views

Maximizing Product of Selected Cards

Jennifer is playing a game. The Ace through King of spades are taken from a standard playing deck and laid out facedown on the table. At any time, Jennifer can select two cards and reveal them, and ...
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9answers
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“We accept 20% of candidates and I'm 90% good at my job…” [closed]

There is a famous investment firm where a partner was known for having candidates walk into the room without a greeting, sit across from him at a huge desk, and start right away by asking: "We ...

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