# Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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152 views

### Finding the numbers [duplicate]

I found a nice problem. Here is what it says: Kevin and Peter are given a piece of paper each where they write a number. Their friend John comes up and takes the two pieces of paper and opens them up ...
136 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

### A Short Dice Puzzle II

A standard $6$-sided die is put inside a cup. The cup is shaken and put upside-down, hiding the die. You are going to guess what is the number on the top of the die. But, instead of given $6$ options, ...
1k views

### A coin flip's long tail

I have a (possibly-) unfair coin, which lands heads with probability $p$ and lands tails with probability $1-p$. I toss it twice; the tosses are independent and identically distributed. The ...
618 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 ...
683 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 ...
848 views

### Best strategy to get all heads/tails from three coins

Your friend has 3 fair coins: a dime, a nickel, and a quarter. She places them on a table behind you. She can arrange then in any pattern of heads and tails as long as they are not all the same. You ...
2k 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. ...
347 views

### Card Passing Game

13 friends are sitting around a table. They shuffle a half-deck of cards, consisting of only the black cards of a standard deck, and deal out two cards to each person. There are then a series of ...
225 views

### Minesweeper challenge #5

Coming back to another Minesweeper challenge... I've run into another "unsolvable corner" (corner of a puzzle where there isn't enough information to be 100% certain that any particular square that ...
267 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 ...
556 views

### Dr. G's Interesting Theorem on Playing Cards

Dr. G has spent his last weekend with analyzing $n$ number of cards which are numbered from $1$ to $n$. He has a fair shuffling machine for his cards and while playing and drawing some cards, he uses ...
441 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

### Probability of three segments forming a triangle

Consider a line segment of length L. This segment is cut in three segments at arbitrary points. What is the probability that these three segments could be rearranged as sides of a triangle?
1k views

### In a Guess The Color game, what's the optimal strategy?

Here's a one-player card game: We begin with a shuffled card deck The player try to guess the color of the card at the top (black or red) If the player guess right, he can keep the card. Else the ...
457 views

### Gambling snap game

You have two shuffled decks of cards (52 cards each). You put them next to each other and deal two at a time, one from each deck. What is the probability that there will be at least one match? ...
187 views

### Optimal guess in a game

Suppose that A and B play a strange game. At the beginning of the game A can choose one real number - $x$ - between $0$ and $60$. Each round of the game goes like this: B names random real number $b$ ...
628 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 ...
301 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... ...
598 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 ...
299 views

### Optimal solution to a modified poker game

Note: Knowledge of the poker game Texas Hold-em is (probably) needed in order to answer this question. You and a friend (only two people are playing) are playing a standard game of Texas Hold-em but ...
152 views

### Probability in Fighting Tournament in which Contestants consume each other

A tournament has 2 teams of 24 people each of weight 1. Each team sends one person into the pit where they fight until one consumes the other taking on all their weight. The probability that one ...
618 views

### Left coin, Right coin, Last coin- A fair version

In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, all players toss their coins together and put it on the table in front of them. Then each ...
333 views

### The Ravages of Purple Spots Disease

While browsing the Internet for medical lore, you happen on a medical encyclopedia article about purple spots disease. Instances of purple spots disease have been documented in 150 countries. The ...
2k views

### A modified version of apples and oranges logic

Question: You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with āApplesā, āOrangesā and āApples and Orangesā. ...
321 views

### 100 prisoners' names in boxes, against smart warden

My question, which I do not know the answer to, concerns the classic 100 prisoners and 100 boxes puzzle, summarized below. The solution to this assumes the names are placed in boxes randomly, and gets ...
282 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 ...
241 views

### Will you win the game?

You play a gambling game. On 100 folded pieces of papers are written 100 different values. You cannot see the numbers written on the folded pieces of paper, which are grouped in a pile. You pay 10 ...
142 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
12k 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 ...
465 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 ...
2k views

### Place 10 Coins Heads Up Blindfolded [duplicate]

You are blindfolded and 10 coins are placed in front of you on table. You are allowed to touch the coins, but canāt tell which way up they are by feel. You are told that there are 5 coins head up, and ...
184 views

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### Does it exist a quick way to find the numbers unseen of two tokens after then have been tossed? [closed]

I'm confused about this riddle. I've tried to guess which numbers could be on bottom, but in the end I couldn't got an answer. Can someone help me please? The riddle is as follows: Over a table ...
262 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 ...
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 ...
49 views

### Knight's Tour Question [duplicate]

A chessboard is an 8 Ć 8 grid. A knight can move up two squares plus one square to the left or right, or up one plus two squares to the left or right. For a knight in the position shown, determine the ...
2k views

### Should I take the antidote? [closed]

A new disease has been discovered in the world, it is called Blue. Statistically 1:1000 people in the world has it and it makes your whole skin blue in a few weeks after getting the disease but not ...
1k 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: ...
406 views

### A game with numbers [closed]

Two people randomly select two different 1-digit numbers (including 0 of course) and calculate their absolute difference. Then They share what they get, What is the probability of having the same ...
364 views

### How to beat Count Dracula, part 2

This is a follow-up to "How to beat Count Dracula". Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. The three players agree on the following rules: Count Dracula and ...