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# Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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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 ...
6k views

### Eccentric Millionaire Probability Paradox

The following is a probability paradox I've been thinking about. It involves Bayes' rule; if you're not familiar, a good starting example is a urn that has a 50% chance of containing one black ball ...
1k views

### How long until all balls are the same colour?

You have a bag containing $n$ balls of $n$ different colours. Select 2 balls randomly (in order, so there's a first and a second), repaint the first in the same colour as the second, and replace both ...
949 views

### Hat Guessing Game in Vegas

A team of 10 people are going to play a cooperative game. While their eyes are closed, a pit boss will place either a red or green hat on each of their heads, chosen by fair coin flip. They then all ...
2k views

### Cooperative guessing game: no incorrect guesses

There are 15 players who will play a cooperative game. They begin by closing their eyes. A referee will place either a black hat or a white hat (chosen by fair coin flip) on each player's head. The ...
417 views

### Queue in the bank

Six men are queuing in the bank when the clerk decides to take a break for 10 minutes! Before leaving, he gives to the six men a numbered ticket, in the same order of the queue (ticket #1 to the first ...
2k views

### Points in a Rectangle

I was asked this question in an interview, so I am not sure what the optimal answer is. But here it goes: Given a rectangle with length l and breadth b, I pick 4 random points inside it. What is the ...
1k views

### Deserted Island [duplicate]

You are stranded on a deserted island with little to no food sources. By your guesses, you will only be able to survive another 10 days. Your only real chance of survival is getting rescued by a boat. ...
2k views

### Who's favored in this dice game?

Alyson and Bethany decide to play a game involving a (standard six-sided) die. Alyson goes first, and rolls the die: if she rolls a 6, then she wins. Otherwise, Bethany takes the die and rolls until ...
1k views

### 4 player card game, who has advantage? [closed]

Edit for "off topic" "correction". I don't know why this question was considered "off topic". It seemed to draw a lot of attention. The "puzzle" was to figure out which person has the advantage ...
827 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....
179 views

### Fumbling with a question already posted

This question, has me stumped. Looking at the first version, how there's two lines of thought that go around in my head, both (seemingly) justifiable. 1 : 'One of them is a girl' implies 'Both ...
569 views

### Ants on a Hula Hoop

There are $24$ ants scattered around a hula hoop of circumference $3$ meters . They each randomly, and independently, choose to face clockwise or counterclockwise, and then simultaneously start ...
799 views

### Another look at the two children riddle

Inspired by this question about the Monty Hall problem, here's a deeper look at another well-known counter-intuitive probability problem which is often stated in a way that leaves subtle ambiguities: ...
4k views

### Monty Hall all over again?

Often, when people ask the Monty Hall problem, they omit some important details, such that the problem becomes ambiguous, or they add more details, such that the problem changes drastically. For ...
131 views

### Compare two numbers by looking at one [duplicate]

Alice takes two envelopes and puts some number of dollar bills in each one. These can be any positive whole numbers (we're putting realism aside), but they cannot be the same number. Bob chooses one ...
2k views

### Hamlet and the theatre

Hamlet is preparing a play to find out the truth about his father's death. The theatre has $2015$ numbered seats and can contain all the members of King Claudius's court. He gives to each member a ...
2k views

### How to maximize your wages?

You're trying to work out how to maximize the wages you receive in the month of February (in a non-leap year). You must work at least 5 days a week and at least 5 hours a day, but you can also work on ...
11k views

### Coin Flipping Game with the Devil

You die, and awake in Hell. Satan awaits you, and has prepared a curious game. He has arranged $n$ quarters in a line, going in the east/west direction. He placed the coins at the ends tails up, and ...
292 views

### Ant walking on a number line 2

I'm going to raise the difficulty of the original question one dimension, so maybe a refresher will be good... Link: Ant walking on a number line I just mentioned i will raise it by one dimension... ...
592 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 ...
1k views

### Cooperative guessing game

A standard deck of 52 cards is shuffled and split into two piles of 26 cards each. Two players cooperate, they must score as many tricks as possible. The first player draw 5 cards from the first ...
1k views

### Clash of arrows

During the last country fair, you have seen a weird arrow-shooter machine. Its shape is a regular polygon with $N$ sides of length $1$ and it fires one bolt from each vertex at the same time. The ...
515 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: ...
6k views

### Ant walking on a number line

An ant walks on a number line, starting at location $x=7$. Each second, it randomly moves one space either left ($-1$) or right ($+1$), with equal chance. At $x=0$ and $x=10$ are drops of honey; the ...
202 views

### It rains in Gadyukino

It rains in Gadyukino village every other day on average. Assume the probability of rain on any given day is 50% and independent. A local weather forecaster has the sole duty every day of predicting ...
9k views

### Three doors, one question

A prisoner wakes up in an empty room (being seated on the floor against the wall). There are three solid doors on three of the room's walls: one to his left, one in the middle in front of him and one ...
262 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 ...
122 views

### duel of 3 people shooting [duplicate]

$3$ people $A,B,C$ are shooting each other. The chance that $A$ will hit in a single shot is $0.2$, The chance for $B$ to hit is $0.3$ and for $C$ is $0.1$. If one hit a person, he will continue to ...
2k views

### Two men for one gold coin

Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails. What is a fair way ...
5k views

### My grandfather's socks

My grandfather has a big drawer where he keeps his socks. The drawer contains more than 900 but less than 1000 individual socks. Each of his socks is black or blue, and there are more blue socks than ...
399 views

### Jewels in the box

Professor Egghead participates today in a local game show. There are six jewels (a diamond, an emerald, a moonstone, a ruby, a sapphire, and a topaz), and there are six boxes that carry the numbers 1,...
367 views

### Probability in chess tournament

In a 4 round chess tournament with 16 players (where the loser of each two player match is eliminated and the winner moves on to the next round), the pairings for all matches are decided randomly. The ...
6k views

### Card probability problem [duplicate]

You have three cards in a hat. One is white on both sides, one is red on both sides, the third is white on one side and red on the other. You pull a card out of the hat and lay it down. The face is ...
301 views

### The Programmers Bot!

Dr. Probot is a famous inventor, known for many creations, his most recent being "Bot". Bot is the very first working robot, he has 3 very basic instructions: Left Right Self Destruct Left: Rotate ...
1k views

### Triangle in a circle

Suppose three points are chosen at random in a circle. A triangle is made with these three points as vertices. What's the probability that the triangle contains the origin of the circle? (Although I ...