# Questions tagged [probability]

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

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### Unpaired socks in my lap

Today in my laundry basket I had 10 distinct pairs of socks. I repeatedly take a sock randomly from my basket. If it matches a sock in my lap, I pair both up and put them aside, otherwise I put it on ...
• 971
521 views

### The HH vs HT question

My puzzle is based on this tweet (image): Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, ...
• 32.5k
1 vote
224 views

### Diamond Rush: Back to... um

It is summer in the Pse School Of Logicians, and everyone studying there is dying for a break (they absolutely hate school, and can do anything to get out of it). And because the teachers there are ...
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### Winning chance in coins game with fixing

A player plays the following solitaire game. The game consists of as many rounds as are needed to produce a result. They have 20 fair coins, which may in any round be live or fixed; each coin starts ...
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732 views

### The Alien Snails Experiment

Fictional Background Story (The Experiment): Two extremely fast and intelligent alien snails are randomly placed on two different points on an infinite plane, as an experiment by the cruel ruler of ...
• 35.7k
135 views

### Picasso at the art school [closed]

Picasso is preparing for his fine art exam. At the exam he will be shown exactly (a replica of) one of the following four paintings chosen uniformly at random: Mona Lisa The Last Supper The Starry ...
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1 vote
151 views

### Impossible Minesweeper?

I was playing the game Minesweeper earlier today and came across the following situation: (Look at the bottom-middle section of the gameboard.) It seems to me that either of the two diagonal pathways ...
• 1,112
422 views

### Does this random sequence contain the number 1?

Randomly choose a number from 1 to 3 and call it $a_1$; Randomly choose a number from 1 to 3$a_1$ and call it $a_2$; Randomly choose a number from 1 to 3$a_2$ and call it $a_3$; $\cdots$ Repeat this ...
• 6,536
158 views

### How many pencils are there? [closed]

Four pencils are chosen (without replacement) from a pencil case, two of which are blunt. The probability that both blunt pencils are chosen is twice the probability that neither is chosen. How many ...
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372 views

### The Monty Hall loot box

Everyone sufficiently competent in probability knows that in The Monty Hall problem as most commonly presented, switching doors wins you the car $\frac23$ of the time. I have come up with this ...
• 7,720
5k views

### What is the probability that your life will have lasted for 100 years once you die?

You are in a world where exactly 90% of all people live for exactly 3 years, and exactly 10% of all people live for exactly 100 years. Aside from what I mention here there is no information that can ...
417 views

### Button multi arm bandit problem

Let's say you have the following buttons to press, labeled a - j, that would earn you the following amounts of money: a: \$6 b: \$9 c: \$15 d: \$26 e: \$45 f: \$78 g: \$136 h: \$416 i: \$728 j: \$...
570 views

### What is the probability I can't bike despite good weather? [closed]

I am trying to solve this puzzle: I have a total of two bikes that I keep at work or at home. I always bike to and from my work unless it rains, in which case I take a taxi (and don't bring my bike). ...
• 111
2k views

### frog on a number line

A Frog is at C. The purple numbers are the probability that the frog jumps in that direction when it is at certain place. The frog stops at A or E. What is the probability that the frog stops at A? ...
• 123
265 views

### Expected number of steps [closed]

There are N cars that are parked in N parking spots numbered from 1 to N. After the Nth parking spot, there are N more parking spots numbered from N+1 to 2N. At each step, a car is selected randomly ...
945 views

### Was Humpty Dumpty right?

Raymond Smullyan's What is the Name of This Book? contains a puzzle which I'll paraphrase here: Of the identical twins Tweedledum and Tweedledee, one of them lies on Mondays, Tuesdays and Wednesdays ...
• 1,536
519 views

### Colliding Bullets again

Here's a colliding bullets problem of my own devising that's different from previous versions. Every second a gun has a 60% chance of firing a bullet in a straight line. After 10 seconds there would ...
• 780
231 views

### Expected power consumed

Suppose you have an 8x8 grid of electric bulbs. So you have 8 rows and 8 columns. Now you can either switch on and supply power to entire row(or column), or switch it off and supply no power at all. A ...
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### Distracted Monty Hall

You're about to compete on the standard Monty Hall gameshow. But immediately before the show starts, you overhear the host's wife telling him she wants a divorce. You estimate that with probability 50%...
• 1,536
787 views

### Replacing Untold Billions

First: Assume Earth's population is 8,037,860,611 and they have ID numbers 1 through 8,037,860,611 You make a set of cards numbered 1 through 8,037,860,611 A robot goes to each person in turn and ...
• 3,818
277 views

### Intransitive urns

N balls with numbers 1,2,3...N are filled arbitrarily into 3 urns A,B and C - but no urn may remain empty. We write P(A,B) for the probability that a ball chosen randomly from urn A shows a higher ...
• 1,649
256 views

### Making fair dice

Dmitry Kamenetsky asked the following two questions: Making two fair dice Making three fair dice My question is a generalization of Dmitry‘s questions. You are given N unlabelled standard 6-sided dice....
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2k views

### Making three fair dice

You are given three unlabelled standard 6-sided dice. Can you write every number from 1 to 18 on the dice, such that in any given throw each die has the same chance of being the highest? Here is a ...
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### Making two fair dice

You are given two unlabelled standard 6-sided dice. Can you write every number from 1 to 12 on the dice, such that in any given throw there is a 50% chance of the first die being smaller than the ...
• 36.2k
434 views

### Measuring distance with steps

I am trying to measure 100m for a children's foot race, but I forgot to bring my measuring wheel. I know that each of my steps is between 0.9m and 1.1m (sampled at uniform). I can only take full steps ...
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253 views

### The minimalist game master [closed]

A game master tells his party of players that he has converted to the school of minimalism, and is going to do away with all of his dice in the campaigns they play from now on. In the place of dice, a ...
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### A prisoner and two dice

A prisoner is offered the following deal. They will be given a pair of standard 6-sided dice to roll. If they can roll a total of 42 or more without rolling a double then they will be set free. ...
• 36.2k
447 views

### Stickered Dice Game

You and your friend play a game. To begin with, each of you has an unlabelled die. On the table laid in front of you are 12 stickers labelled 1-12. The first player chooses one of the stickers and ...
• 175
730 views

### The Halftime Hustle

In a soccer stadium restroom there are 100 stalls (cubicles), arranged in a straight line. Stalls are numbered 1, 2, 3,..., 100, with 1 being closest to the main exit of the restroom. Unfortunately, ...
• 1,083
178 views

### Grabbing enough M&Ms to be 80% confident all colors are represented [closed]

Assume you have an arbitrarily large jar of M&Ms, with six different colors of M&Ms present in equal quantities. If you reach into the jar and grab a fistful (what we'll call a "pull"...
• 233
158 views

### How many earrings do you have to pick up? [closed]

I'm having trouble solving a puzzle in Swedish. I've translated it below: How many earrings do you have to pick up to be sure to get a pair of the same in a mix of earrings where "favorable ...
1k views

### A series of rock-paper-scissors games

You are playing a series of 100 games of rock-paper-scissors^ against your friend. From your past games, you know that he will choose exactly 40 rocks, 35 papers and 25 scissors in some random order. ...
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201 views

### In an infinite maze of squares with p% walls, will you be boxed in?

If you are in an infinite maze of squares, where each border between two squares has a $p$% chance of being a wall, what is the probability $F(p)$ that you are trapped in a finite space? For a better ...
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252 views

### Good and bad numbers of remaining mines

You've been tasked with finishing solving this Minesweeper board: "How many mines remain?", you ask. "I'm just choosing that now, actually. Tell you what: I was going to consider every ...
1k views

My niece, a medical consultant, sees a number of patients every day, and the first thing she asks is for their birthday. Recently, in a certain week, patients 16 and 17 shared the same birthday (...
1 vote
264 views

### Mastermind algorithm but for unique colors only

I have seen Donald Knuth's Algorithm to guess the correct pattern in maximum 5 tries. However, I want to write a program to find the correct pattern effectively however the code maker can only make a ...
526 views

### Prisoners, apples & oranges

You are in a group of sixty prisoners, and the warden has a game to play with you. In a room there are sixty boxes. Each box can contain either two apples, two oranges or one of each, but you don't ...
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546 views

### Two cornucopias and infinitely many gold coins

There're two cornucopias of infinite volume, each with one gold coin in them. Right now $t=0$. A new coin will be born at $t=\frac{2^n-1}{2^n}$ for every positive integer $n$. Each new born coin will ...
• 6,536
174 views

### Puzzle regarding 100 random objects of different sizes, and choosing one at random one at a time to get largest

Basically, the riddle at hand was used to demonstrate a principle (of which I forgot), and it was asked thusly; I know there are other forms of it, but here goes: You are fishing in a pond of 100 fish ...
924 views

### Gold and silver coins in sealed envelopes

Alice has freely chosen to put either a gold coin or a silver coin in each of an infinite sequence of envelopes numbered 1,2,3,... Bob can open any number of envelopes and check the coins within, ...
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135 views

### What is the name of this problem about maximizing the accepted offer from consecutive offers?

There was a problem I have read more than 15 years ago. I just remember the problem and the rough outline of the solution, and I would like to know if it has a canonical name to look up the ...
627 views

### rope - knotted or does not knot [closed]

The figure shows the shadow of a piece of rope on the ground, and you can't see which part is on which part; Suppose the rope is placed completely randomly. Now tighten the two ends of the rope to the ...
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3k views

### Yet Another Card Payoff Game

From A Practical Guide to Quant Interviews: A casino offers yet another card game with the standard 52 cards (26 red, 26 black). The cards are thoroughly shuffled and the dealer draws cards one by ...
• 635
1 vote
269 views

### Bullets in russian roulette

I see a similar question in Russian roulette. Now if instead of two bullets being placed side by side, two bullets are randomly put in the chamber. Your opponent played the first and he was alive ...
• 635
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### If the door in Monty Hall is opened by a person without knowledge of where the prize is, and also does not reveal prize, do the odds change?

Here is the quiz variant. After the candidate chooses one door for the first time, and before the master (who knows which door hides the prize) intentionally opens another one to reveal no prize, an ...
1 vote
192 views

### The Truth And Lies Today: Revisited

A man is only capable of telling the truth four hours a day. They are either TTFTT or TFTTT (equiprobable). For the other twenty hours, he lies. All hours between 7pm and 6am are night; 7am and 11am ...
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1 vote
206 views

### The Truth And Lies Today

Suppose a man only tells the truth three hours a day. It is the same every week and it is known that the pattern of the truth hours are TFTFT. (which means he may tell the truth at midnight and 2am ...
• 1,100
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### Who is most likely to win all the chips?

Alice, Bob and Charlie each have 5 chips. Starting from Alice, they take turns to act in the order of Alice, Bob and Charlie. The $n$-th person to act must take a total of $n$ chips from their ...
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436 views

### I'm not a robot, I'm not a MONKEY

The city of Roboville has been invaded by robots, monkeys, and dancers, who will dance if the beat's funky. Some of the invaders can be two of them (e.g. both monkeys and robots) and some can be all ...
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