Questions tagged [probability]
A mathematical puzzle whose essential nature involves randomness. Use with [mathematics]
411
questions
5
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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?
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2
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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 ...
3
votes
3
answers
774
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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 ...
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7
votes
3
answers
486
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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 ...
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3
votes
1
answer
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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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21
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6
answers
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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%...
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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 ...
- 3,783
7
votes
1
answer
266
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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 ...
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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....
- 4,373
8
votes
2
answers
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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 ...
- 31.6k
9
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6
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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 ...
- 31.6k
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1
answer
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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 ...
- 31.6k
2
votes
1
answer
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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 ...
- 2,172
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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. ...
- 31.6k
8
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1
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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 ...
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6
votes
3
answers
717
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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, ...
- 1,038
2
votes
1
answer
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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"...
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votes
1
answer
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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 ...
- 93
6
votes
3
answers
1k
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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. ...
- 31.6k
5
votes
0
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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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2
votes
1
answer
235
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 ...
7
votes
2
answers
1k
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The Birthday Paradox, revisited
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 (...
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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 ...
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votes
2
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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 ...
- 529
8
votes
2
answers
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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 ...
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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 ...
- 3
10
votes
0
answers
582
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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, ...
- 5,890
2
votes
1
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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 ...
3
votes
3
answers
604
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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 ...
- 101
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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
1
answer
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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
6
votes
3
answers
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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
1
answer
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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
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1
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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 ...
- 529
14
votes
2
answers
661
views
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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votes
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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 ...
- 529
0
votes
1
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Will Romeo meet Juliet? [duplicate]
Romeo and Juliet try to meet each other everyday at a certain place between 12:00 and 13:00. They arrive at the place at a random time between 12:00 and 13:00 and they wait 15 minutes (but never after ...
- 355
7
votes
1
answer
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Bertrand's Ballot Theorem
A total of X voting papers for candidate A and Y voting papers for candidate B were cast in one section during the election. Where X > Y
At the end of election day, the voting papers were counted ...
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votes
1
answer
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Follow the randomly-bouncing ball
We are going to generate information out of nothing (well, nothing and a bit of something) just by randomly bouncing a ball. The result will be a message you can use to protect humanity.
Let's use ...
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1
vote
2
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What's the correct intuition behind the expected number of die rolls until a 6 if all previous are even? [duplicate]
I came across a puzzle on YouTube recently (spoiler).
You roll a fair dice until you get a 6. What is the expected number of rolls, including the roll of 6, conditioned on the event that all previous ...
- 22.7k
2
votes
2
answers
392
views
Choose the wine
I based this on a problem from a mathematics presentation, adding a small twist. I did not readily find it here.
Your friend comes to dinner and you know he loves to drink Beaujolais. You have 'Cote ...
2
votes
1
answer
163
views
Hitting twice with different choices
This game of two players has public parameters an integer $n\ge2$, and a probability $p$ with $1/n<p\le1$. E.g. $n=4$, $p=1/3$.
In the first phase of a game, a player secretly decides $n$ ...
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1
answer
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Probability that there will be no mutual best friendships? [closed]
Here is a problem:
There are two groups of n users, 'A' and 'B'. Each user in A is friends with those in B, and vice versa. Each user in A will randomly choose a user in B as their best friend and ...
12
votes
2
answers
1k
views
Can a fair coin be used to simulate an arbitrary weighted coin, with on average only two flips? [duplicate]
This puzzle was told to me by a Stanford PhD student in a graduate course on randomized algorithms. It's really clever/beautiful, and I think makes for a great challenge.
You are given a fair coin, ...
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4
votes
2
answers
368
views
A simple guessing game
You and your friend play a simple guessing game. Your friend thinks of a secret whole number between 1 and 10, inclusive. If you ask your friend what the number is, the following happens:
With 80% ...
- 31.6k
2
votes
2
answers
285
views
Gambling game where you pick how many coins to flip
At a gambling joint, you are invited to be a player in a game with identical unfair but consistent coins flipped simultaneously in each round, with no cost to enter. Each player gets a different ...
- 1,798
9
votes
1
answer
374
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Probability that D wins this contest
Problem: $A, B, C, D$ are playing an archery game. They have equal probability of landing their arrow on any spot the target with radius of $R$. Their score is the distance to the center of the target....
1
vote
2
answers
431
views
A certain 'Monty Hall' variant was played. How many doors were there, and, what was the value of the prize?
Recall the standard Monty Hall scenario where a presenter hides one prize with high value $h$ behind one closed door (e.g., in the classical version: the one high prize is a car), and, equal prizes ...
16
votes
6
answers
3k
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Three horse race
There are three horses in the race. You know the following information about them:
Horse A will finish the race in 50 or 60 seconds with both events being equally likely.
Horse B will always finish ...
- 31.6k
0
votes
2
answers
155
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How can we allocate when we have 150 open slots every day (5 days a week) for those 200 arrivals every day
My question is to solve a very basic problem related to the allocation of slots. Say there are 20 teams with 10 persons in each team.
I have 150 open slots every day (5 days a week) for those 20 teams ...
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