Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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6
votes
2answers
220 views

A very tiny probability puzzle [closed]

Imagine there are six football teams (A,B,C,D,E,F). They play each other in a league once only (on neutral ground). To determine the score, two $d4-1$, i.e. the outcome is $\{0,1,2,3\}$ are rolled, ...
2
votes
1answer
98 views

Four unfair dice

On a table there are four standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each. Alice starts and chooses a die. Then Bob chooses a die and both throw the dice. The winner is the person ...
1
vote
1answer
111 views

Banknotes recalling [closed]

Last year the inhabitants of Elfland (which are -of course- Elfs) had a referendum and decided to stop using barter and to adopt their own currency (the Elfcoin). On January 1st, 2020 the central ...
4
votes
2answers
445 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? ...
3
votes
1answer
159 views

Two dice with same probability for each sum mk2

Inspired by Two dice with the same probability for each sum? To cheat in a game of sums, you get yourself a pair of magic dice. That pair behaves in a wonderful way where each individual die is fair (...
5
votes
6answers
1k views

Two dice with the same probability for each sum? [duplicate]

A friend invites you to play a game. The game is using two standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each. As usual, the dice are considered distinguishable, i.e. throwing a 1 with ...
8
votes
1answer
244 views

Maximizing Product of Selected Cards

Jennifer is playing a game. The Ace through King of spades are taken from a standard playing deck and laid out facedown on the table. At any time, Jennifer can select two cards and reveal them, and ...
9
votes
3answers
390 views

A box full of unfair coins

Lolek and Bolek are arguing on whose turn is to take out the trash. They have a box with $n$ coins. when the coin $i$ is thrown, the probability that it lands on heads is $p_i$. They decided to make ...
1
vote
3answers
191 views

Blood Type Puzzle 2: Am I Pure Blood?

This puzzle is similar to the first puzzle but with a few twists: In this question: both my mom and I are blood type B. But this time I don't know my dad's blood type. My mom said her parents ...
3
votes
3answers
241 views

Blood Type Puzzle 1: Am I Pure Blood?

If my parents (biological) and I all have blood type B, how likely am I a pure blood? (expressed as a percentage) Follow up question: If my dad is blood type AB instead of blood type B, and ...
6
votes
1answer
295 views

Russian Roulette (Redux!)

You are challenged to a game of Russian roulette with a six-chamber revolver, but you and your opponent are allowed to change the outcome of the game in different ways. Here's how the game will ...
1
vote
2answers
236 views

Find the least number of objects from a jar when those have two colors

I've been going in circles with this question which belongs to certainty about something. The original source of this problem is unknown. I found it in a textbook who doesn't have an author but rather ...
-3
votes
2answers
152 views

Chef wants to play [closed]

You are very hungry and decide to visit a restaurant with a couple of friends. You want to order three dishes for the three of you. But, the chef serves you only if the total cost of the dishes ...
1
vote
1answer
90 views

Variation of Monty Hall problem for gambling on who is the champion soccer team

So let's say, if you can guess who the champion team is for soccer, such as in World Cup, then you win a car. Otherwise, you win a goat. There are 4 teams left. Country A, B, C, and D. And country A ...
7
votes
3answers
157 views

Playing Chess Game of Chance

I still enjoy playing chess at the age of ninety four.Those contemporary opponents I used to play with have all passed away without me even getting even scores with any of them. On my spare time I ...
0
votes
2answers
235 views

Witches' Coffee [closed]

Two witches make a nightly visit to an all-night coffee shop. Each arrives at a random time between 0:00 and 1:00. Each one of them stays for exactly 30 minutes. On any one given night, what is the ...
2
votes
1answer
154 views

Sleeping Beauty Study at the Institute of Mad Science [closed]

You've been approached to assist in the furtherance of SCIENCE as a research subject at the Institute of Mad Science (local branch)! The experiment you'll be involved with is called the Sleeping ...
16
votes
3answers
1k views

Box of tablets, whole or broken: solution required

This is a puzzle that I thought up whilst taking a course of meds. I currently haven’t solved it, and would be curious to know if anyone has a solution for it. Here goes: Scenario: John has a box of ...
1
vote
1answer
81 views

Chess Puzzle to calculate the minimum number of movements of pawn [closed]

Given an N×N chessboard, with two pieces, a black pawn and a white pawn randomly placed on the chessboard. What is the minimum number of steps required by the white pawn to reach the black pawn under ...
10
votes
1answer
308 views

Birthday girl's casino game

My daughter's birthday is coming up. Here's a fun party game we can play to celebrate. (Bring your wallet!) I have a pair of 6-sided dice, and a standard deck of 52 cards. You place your ...
5
votes
3answers
194 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'...
1
vote
3answers
235 views

Jack and Jill went up the Hill to play

A Simple Card Game. This deck of cards has only four cards simply labeled 1, 2, 3, 4. They are placed face down. Jack and Jill take turns to draw a card. You sum up the numbers drawn so far after ...
5
votes
1answer
210 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 ...
2
votes
3answers
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 ...
5
votes
2answers
210 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 ...
0
votes
1answer
78 views

Place Your Bets 3 , last of the series

A harder sequence to figure out... What are the next 4 cards, including suits?
1
vote
1answer
52 views

Place Your Bets 2 - In sequence, of course

Your Cards... You have to figure out what the next row of 4 cards will be. There is a pattern in there somewhere, promise. Good Luck
12
votes
12answers
5k views

Coin Game with infinite paradox

Here’s the puzzle/problem: Let’s presume we are best friends. I own the house next to you. I make a gaming proposition along the following lines: You throw a coin over and over again. So long as it ...
4
votes
2answers
290 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 ...
43
votes
11answers
8k views

3 doors, three guards, one stone

You are in a room with three doors. Behind two of them, the darkest pit of hell waits for you to make a mistake. The other door leads to heaven and freedom. Each door is guarded by a guard: Michael, ...
17
votes
5answers
925 views

Blindfold Bingo

Congratulations, you have been selected from among the audience to compete in the fabulous Blindfold Bingo challenge! (cue annoying, yet catchy theme music.) Here you see our perfectly ordinary Bingo ...
16
votes
5answers
2k views

Monty Hall variation

During a train trip I cooked up a semi-autobiographical variation of The Monty Hall problem for people who already know the original. Perhaps it is more of a meta-puzzle than a puzzle, but I hope it ...
5
votes
2answers
832 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 ...
4
votes
2answers
217 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 ...
9
votes
5answers
1k views

How long will my money last at roulette?

I'm at the casino, standing next to a roulette table with a \$10 minimum bet. I want to stay here as long as possible, so I'm going to repeatedly make the minimum bet until I run out of money. I'm ...
6
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 ...
1
vote
1answer
90 views

Meeting of 2 Drunk Walkers (Random Walk) [closed]

There are 2 drunk guys who walks according to a Random Walk. Each of them, with equal probability of $ 0.5 $ turns either right or left. They both start at the origin and their turns are synchronized ...
5
votes
1answer
110 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
6answers
391 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 ...
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
182 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
0answers
230 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 ...
10
votes
1answer
3k views

Lost first game – can I still make my mother proud?

I am one of the greatest finger wrestlers of my generation. Only 0.1% of all players are better. When I play against someone who's worse than me, I win 99% of the time. Against someone who's ...
19
votes
8answers
2k views

A Short Dice Puzzle

There are $2$ fair dice: An $11$-sided die, valued from $-5$ to $5$, A $41$-sided die, valued from $-20$ to $20$. You pick one, and I'll take the other one. We roll the dice, and whoever rolls the ...
4
votes
2answers
148 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 ...
6
votes
3answers
566 views

Monty's Labyrinth

(A fun combination of two classic puzzles, hope seasoned puzzlers enjoy.) Having escaped through almost all of a labyrinth, you are met by three magical doors. Two of them lead to certain and ...
13
votes
5answers
1k views

Olivia's cookie jars

Olivia loves cookies so much that Dad promises to buy her two cookie jars on one condition: that she only eats one cookie per day. Olivia agrees, and now two black, large cookie jars rest on the ...
10
votes
3answers
653 views

Fight Battle 21

Based off a very, very well-known puzzle The new RPG, Fight Battle 21, is now here! Now with the same three characters as the previous 20 editions! Knight: 6 HP, 60% chance to deal 3 damage Archer: ...
2
votes
2answers
95 views

Risk Appetites - betting percentages

This question is from the September/October issue of the Actuarial Review magazine. Kim and Ann start with an equal amount of money, but they value money very differently. Kim acts to maximize the ...
61
votes
15answers
10k views

2 Monkeys on a computer [closed]

(a) Two monkeys are typing capital letters (A-Z) randomly. The first stops typing when the word COCONUT appears as seven successive letters. The second stops typing when TUNOCOC appears; TUNOCOC is ...

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