Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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-4
votes
2answers
234 views

Random chord to a circle around a triangle

This puzzle is literally a math textbook question. Its only redeeming feature is that it also happens to be too broad in a surprisingly interesting way. The problem Given the circle $\mathbf O$ ...
32
votes
7answers
5k views

Monty Hall Revisited: Winning Both Goats!

Suppose you're at a game show, knowing the winning strategy for the classic Monty Hall problem. Your turn comes up and you take the stage. You confidently choose door number (?). Just as you are ...
11
votes
2answers
845 views

Expected Number of Tosses Until H,T,T,H

I found a nice little app/game the other day called Probability Puzzles. Apologies to those who, like me, will now obsess until they are all completed. I'm sure there will be many such people on this ...
8
votes
2answers
1k views

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 ...
4
votes
3answers
517 views

Lottery in Minesweeper

The question is inspired by this scenario: In this case, we had 2 tiles remaining, and each had the equal probability of being a mine, based on the already deduced information. Thus it was necessary ...
15
votes
2answers
484 views

“Musical chair” for clock hands

A colleague and me usually make bets on the time when a simulation is finished. Next time I would suggest the following: At the time the simulation is finished we take a look at the analog clock on ...
9
votes
2answers
606 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 ...
1
vote
2answers
162 views

Landing 4 on a Broken Die [closed]

This is not hard, but fun. Suppose you have a die such that its 1,5,6 and 4 face are broken. Whenever 1 face lands, it gets rolled over to an adjacent face. If 5 face lands, it is equally likely that ...
45
votes
7answers
9k views

How many tries to roll a 6?

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ...
6
votes
3answers
359 views

Guessing game with infinity coin flips

Evan and Ollie are going to play a game as a team. The two friends placed in separate rooms, and then a coin is flipped infinitely many times*. Evan is told the results of the even numbered flips, ...
5
votes
1answer
238 views

An island, a boat, and a roulette

You are on an island where a volcano is going to erupt anytime soon, wiping everything with it. The only way to leave the island is via boat, but the captain of the boat asks 80 £ for the ride. You ...
0
votes
1answer
81 views

Taking a ball from basket challenge [duplicate]

I have 10 red balls, 10 blue balls, and 2 baskets. You are free to choose the numbers of red balls, and the numbers of blue balls to put to the first basket. Then you have to put rest of the balls to ...
6
votes
2answers
762 views

Drawing balls from a pocket

I have a pocket of N=4 balls of different colors, say green, red, blue and yellow. You can draw as many times as you want After each draw, the ball will be put back to the pocket so that the chance ...
2
votes
2answers
309 views

A Shooting Target with 9 shots

You are a soldier in the army, and the commander is testing his soldiers for their shots. But the commander is also a mathematician and would like to test not only your shooting ability but also your ...
7
votes
2answers
2k views

Find Coin's unfairness with only 4 tosses

There is a unfair coin and you want to find out its actual probability, to find the exact probability is actually not an easy task, you need to toss it many many times to get the close to actual ...
10
votes
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 ...
6
votes
2answers
605 views

Probability of nobody being born in a specific month

Assume 11 persons are born in 11 different months. What is the probability $P(n)$ that none of them is born in the $n$-th month? This would be pretty easy if all months had the same length, then $P(n)...
3
votes
2answers
365 views

The most probable key

You broke into John Doe's house and found the safe. It has a combination lock with 4 dials ranging from 0 to 9 each. ...
-3
votes
5answers
228 views

Interesting card combinations [closed]

In a normal pack of playing cards (without jokers), the probabilities of the following events are the same: (1) Drawing a set of 4 different cards (irrespective of its color and suit) - let us call ...
2
votes
1answer
160 views

Dice problem involving nine randomly selected cups [closed]

I was given this problem by a colleague, and I cannot figure it out. Given nine cups and an unlimited supply of six-sided dice rolled one at a time, what is the probability that you will, at some ...
8
votes
2answers
542 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 ...
22
votes
3answers
4k views

bored of eating soup

A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating. When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game ...
4
votes
3answers
586 views

Effective strategy for prisoners to see movie

100 prisoners are given an opportunity to go to a theatre and watch a movie. Each can choose either to go or not. However, if everyone chooses to go to the trip then no one is allowed to go. The ...
9
votes
4answers
435 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 ...
4
votes
3answers
654 views

What are the odds for the student to be right? [duplicate]

If a student answers this questions randomly, without thinking, what are the odds he will get the question right ? 25% chances 1 in 2 chances 75% chances 1 in 4 chances EDIT : This question is not ...
14
votes
2answers
5k views

How to simulate one die with three dice?

I do not know if there is a correct solution to this puzzle, but I can't stop thinking about it, so here goes: is it possible to accurately simulate a single, fair, six-sided die using three custom ...
1
vote
1answer
164 views

Another Unconventional Dice Blackjack game - is Nash equilibrium here?

This question is similar to This Dice Blackjack game - is there Nash equilibrium?, but the game rules are completely different. This Dice Blackjack is game for two. It is also played with fair six-...
0
votes
3answers
369 views

This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
1
vote
1answer
155 views

Simple probability game [closed]

You are asked to play a classic shell game with two shells. Each round, a ball is placed under one shell, the shells are rapidly, continuously rearranged for 15 seconds with distraction*, and then ...
1
vote
2answers
442 views

The Trump Brotherhood

If you happen to meet two of the Trump brothers from the family that lives down the street from you (assume that the two are random selections all of the Trump brothers), it is an even-money bet that ...
2
votes
1answer
120 views

Can you build a Rubik's Cube? [Part 2]

You are given an disassembled Rubik's cube (Detachable centers,corners and edges). You are then blindfolded. If you assemble the cube while being blindfolded. What is the probability that the cube you ...
6
votes
1answer
909 views

cheating on the Russian roulette

This question is inspired by this one. You and your opponent play Russian roulette with two bullets. Quoting from the linked question: You are challenged to a game of Russian roulette. Your ...
5
votes
2answers
833 views

probability tricky question

Nils has a telephone number with eight different digits. He has made 28 cards with statements of the type “The digit a occurs earlier than the digit b in my telephone number” – one for each pair of ...
2
votes
0answers
174 views

German Tank Problem [closed]

"Alright," says the commander gruffly. I try not to stare at the biscuits in his beard. "This week we've captured 5 German VX-Tanks, with serial numbers numbers 3, 5, 13, 22, and 27. They stopped ...
3
votes
2answers
317 views

Return to the Minotaur's Labyrinth

This is an extension of the puzzle The Minotaur's Labyrinth which is inspired by the comments from histocrat. You are trapped (again) in a chamber at the center of the minotaur's labyrinth. There are ...
6
votes
2answers
407 views

Twin Probabilities Problem

1 in 8 sets of twins are sets of identical twins. While talking to Jessica, you learn that she has a twin named Emily. What's the probability that Emily and Jessica are identical twins? The answer ...
-6
votes
5answers
139 views

Underpants in a Drawer [closed]

I have 22 underpants in the drawer and it is dark and I cannot identify the colors. 3 pairs are red. What is the probability of my putting on a red pair of underpants from the drawer? 3/22 is the ...
2
votes
1answer
256 views

2 aliens walk on a line meeting probability [closed]

2 aliens walk on a line randomly. At each timestep they walk independently either left or right (1 meter) with equal probability. They start 10 meters apart. What's the probability that after 7 time ...
5
votes
5answers
357 views

Russian roulette

You are challenged to a game of Russian roulette. Your opponent places two bullets side by side in a six chamber revolver and spins the chamber. She explains that the game is single turn-based and ...
-6
votes
1answer
261 views

The Puzzling Phone [closed]

The amazing "Puzzling Phone", comes in two models, one sold by "Super Puzzling Inc", and one sold by "Mega Puzzling Ltd" Phones need to have government testing before they can be sold on the market. ...
1
vote
0answers
126 views

Tic Tac Toe and random turn puzzle [closed]

I have a problem: There is a bag of 75 balls with 15 Red and rest Blue. I pick 4 balls at the start of every turn.If I get to pick at least 1 red ball, I fill 1 cell with X. If I get 3 red balls ...
0
votes
1answer
926 views

100 coins (Heads and Tails) [duplicate]

"You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can't feel, see or in any other way find out which side is up. ...
-4
votes
3answers
116 views

What is the probability that no one will get his envelope? [closed]

You are given 100 addressed envelopes and 100 addressed letters to be inserted into the envelopes. If the letters are inserted randomly into the envelopes, what is the probability that no letter will ...
0
votes
2answers
552 views

Open doors brain teaser [closed]

There are three doors before you, of which only one is correct. Each door will take you one minute to open by default, but one of the incorrect doors contains a trap that will slow opening of any ...
3
votes
5answers
454 views

Why is my car always in the slowest lane?

Staying in the traffic again this morning, I decided to find a mathematical motivation behind me always being in the slowest lane. Consider the following formalization: there are 4 empty lanes and ...
7
votes
3answers
503 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 possible), but it ...
4
votes
2answers
551 views

The Monty Hall Arena

Monty Hall had enough of all these pesky mathematicians winning cars. Quite demotivated, he modified his show: There is a finite number $n$ of doors There is one car behind a door, otherwise there ...
7
votes
1answer
648 views

Will You (Yes, You) Decide The Election? [closed]

You are the only sane voter in a state with two candidates running for Senate. There are N other people in the state, and each of them votes completely randomly! Those voters all act independently and ...
-4
votes
1answer
174 views

Bad mouse, good mouse [closed]

In a certain city, there are only two companies (called Company A and Company B), that manufacture computer mice. The computer mice from Company A last $x$ hours before needing to be recharged, ...
11
votes
3answers
1k views

A hat puzzle involving wizards

Two wizards, Alice and Bob, each have two hats on their heads. Each hat is independently black or white with probability one-half. When the game starts each wizard will see the hats on the other ...