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Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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4
votes
2answers
270 views

Minesweeper challenge #2

Again, I seem to have run into another situation where there doesn't seem to be a definitive set of squares to tap to solve a Minesweeper puzzle. What squares should I tap to maximize my chances of ...
3
votes
2answers
237 views

Is there a definite answer to this Minesweeper puzzle? If not, which square has the best chance of being safe?

I was working on solving an Expert puzzle in Minesweeper, but came across a hurdle in this corner (the top left). Is there a definitive solution to the problem? If so, what is it? If not, which ...
-3
votes
1answer
104 views

max possible number of dice throw [closed]

Scott repeatedly rolls a pair of standard six-sided dice and keeps track of the sum of the two numbers rolled each time. So far he has not rolled any sum twice. What is the maximum possible number of ...
6
votes
1answer
202 views

Get 20 points from a target board

A target board consists of four parts, and each part has different numbers on it. You will make at most $10$ shots, and every shot's point will be added to your score. If you get a score of $20$ ...
13
votes
3answers
383 views

Guffin factory regulated heist

I work at a guffin factory. I manufacture guffins and have an unlimited access to guffin storage. I can fit up to 20 guffins in my bag, get them home from the factory and nobody will chase me. You ...
6
votes
6answers
5k views

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 (...
5
votes
3answers
352 views

Probability of Girl or Boy

Suppose that I have a friend whose name is X. X has an elder brother who got married 10 years before. But X being a silly guy has the habit of forgetting things; you can say a “Short time memory loss”....
4
votes
2answers
139 views

3 points on a circle [duplicate]

There is a circle where you put 3 points randomly on it as shown below: What is the chance of these randomly chosen three points passing on an half circle? Reference: Bilim Teknik Dergisi 2018-07
13
votes
4answers
3k views

A dice game, what is the optimal strategy?

Alice was walking on the street when she came across a man playing with a die. She could not help trying to check if the die was loaded and while she was concluding that it wasn't loaded, the man ...
3
votes
0answers
110 views

Variation of Boy/Girl Birth Problem [closed]

Parents keep having children until they have one girl, at which point they stop; and babies are girls with probability 0.49. If we select a child uniformly at random (from the entire population of ...
4
votes
1answer
250 views

How likely is a comeback in basketball?

For this most recent NBA season, ESPN.com has had in-game win probabilities: My question: Say a team gets a big lead and has a 90% chance of winning. What is the probability that at some point ...
10
votes
7answers
515 views

A cooperative guessing game - Guess your order and card

6 players sitting in a circle and each assigned a card among 2 Hearts, 3 Hearts, ..., Ace Hearts (i.e. any of the Hearts cards). Holding her card above his forehead (i.e. Indian Poker fashion), each ...
8
votes
5answers
443 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 \...
1
vote
2answers
242 views

What are the chances on watching the clock? [closed]

This is a relatively straightforward little puzzle, but the answers are somewhat unintuitive or can prompt a new perspective. It might be an interesting little puzzle for a probability teaching ...
5
votes
3answers
511 views

Foolproof double betting

Just made up a problem. Have ideas, but no proof yet – came here for professional help. Tonight an important match of Metagame (box/football/baseball/chess) takes place. Everyone is hyped. Everyone ...
-4
votes
2answers
264 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 ...
12
votes
2answers
1k 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
568 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
533 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
648 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
164 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 ...
44
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
376 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
239 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
82 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
766 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
311 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
618 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
377 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
230 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
575 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
589 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
445 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
660 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
176 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
416 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
158 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
443 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
123 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
1k 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
844 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
187 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
325 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 ...