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Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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6
votes
1answer
199 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 $20$ ...
6
votes
1answer
397 views

Corollary to “A game with 52 cards”

Inspired by A game with 52 cards Alice and Bob play the following game with two (identical) standard decks of $52$ cards. First Alice secretly arranges one deck of $52$ cards in a long row ...
6
votes
2answers
752 views

The Fanatic Fever(twist on the 5 pirates puzzle)

While raiding a tropical island, 6 pirates have an incredibly unlucky day. While they scoured the island in search of treasure, one of them was infected with the Fanatic Fever, a disease which hits ...
5
votes
5answers
3k views

This Website Needs More Cat Pictures?

I love cats! And I love browsing cat pictures! :3 I stumbled on a webpage that shows random cat pictures every time I refresh the page. (For example, this site.) It has a database of $N$ cats ...
5
votes
5answers
364 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 ...
5
votes
4answers
3k views

Are you Really Smart

The government has introduced a standardised test to identify dumb people and make them ineligible to apply for any government jobs, a pass in the exam is mandatory for applications in future. It ...
5
votes
2answers
837 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 ...
5
votes
4answers
4k views

make a green profit in roulette

Story You meet a rich drunk CEO at a roulette table in Vegas. She explains to you that she has a way of almost guaranteeing a profit at this game by betting on only black. In the process she gets ...
5
votes
7answers
6k views

Help understanding the solution to a “shooting puzzle”

I need help understanding the solution to the following puzzle: Puzzle: There is a "triangular" duel between the three shooters. Everyone shoots one by one, can shoot once and any person he wants. ...
5
votes
6answers
386 views

A Gambling Problem You Would Love To Have

Let's play a quick gambling game You are going to start by betting a penny, and then I roll a 10-sided die. It is labeled 0 through 9. Whatever you roll, that's what I multiply your bet by and give ...
5
votes
2answers
823 views

How many cookies does someone need to grab to be certain to obtain a flavor?

I often found this riddle in many exams but I got often confused on how to tackle it. While it involves maths. I wonder if there is a subtle or a more layman method to obtain an answer using common ...
5
votes
3answers
350 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”....
5
votes
3answers
977 views

Domino tile possibilities

I own a normal domino game with 28 tiles. Each tile carries two of the numbers [0, 1, 2, 3, 4, 5, 6] (where 0 represents blank). During cleanup five pieces fell out of the box. Two of them showed ...
5
votes
1answer
542 views

The Minotaur's Labyrinth

You are trapped in a chamber in the center of the Minotaur's Labyrinth. There are $\mathbf{N}$ tunnels, $\mathbf{m}$ of which lead to safety; the remaining tunnels only lead back to the chamber. Each ...
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 ...
5
votes
1answer
105 views

Puzzle creation problems using unbounded unknown numbers

I occasionally see puzzles that include language like this: You go to buy a specific car, whose fair price we’ll call N. You have absolutely no idea what N is Or this from the same site: Given ...
5
votes
3answers
505 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 ...
5
votes
2answers
203 views

SafeCracker #2 - The Mission Continues

Thanks to an alert StackE user, we were able to get the first safe open. Mission Details This next safe is in a former employee's house. He is gone for now, so we have no time to spare. We weren't ...
5
votes
3answers
188 views

When is the truth spoken?

A thief speaks truth two days a week alternatively ( T F T ). The days are the same for each week. The thief gives these statements on 3 consecutive days : D1 : I lie on Monday and Tuesday. D2 : It'...
5
votes
1answer
193 views

Answered it badly…on purpose?

Teacher: You got a 0. Miles Morales: Is that...failed? Teacher: Listen. If you answer all questions on a multiple choice test randomly, you would get a 25%. This means the only way for you to ...
5
votes
0answers
147 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 ...
5
votes
0answers
131 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 ...
4
votes
4answers
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 $6$ ...
4
votes
2answers
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 ...
4
votes
3answers
588 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 ...
4
votes
3answers
658 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 ...
4
votes
6answers
813 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 ...
4
votes
5answers
1k 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. ...
4
votes
2answers
334 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 ...
4
votes
2answers
213 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 ...
4
votes
1answer
242 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 ...
4
votes
3answers
541 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 ...
4
votes
4answers
417 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 ...
4
votes
3answers
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 ...
4
votes
2answers
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?
4
votes
2answers
174 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 $b$ ...
4
votes
3answers
552 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 ...
4
votes
2answers
292 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... ...
4
votes
1answer
955 views

Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong ...
4
votes
2answers
559 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 ...
4
votes
2answers
274 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 ...
4
votes
2answers
146 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 ...
4
votes
2answers
324 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 ...
4
votes
2answers
595 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 ...
4
votes
2answers
262 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 ...
4
votes
2answers
260 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 ...
4
votes
0answers
222 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 ...
4
votes
2answers
138 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
3
votes
15answers
9k 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 ...
3
votes
5answers
456 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 ...