# Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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441 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? ...
154 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 (...
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 ...
385 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 ...
235 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 ...
190 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 ...
236 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 ...
234 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 ...
291 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 ...
433 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 ...
2k views

### Three 50/50 guesses

Three friends enter a quiz-show as a team, the final round of the show is all or nothing, they only get their prize if they can win this round. Three boxes labelled 1, 2 and 3 are placed in a room, ...
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, ...
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 ...
86 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 ...
153 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 ...
220 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 ...
153 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 ...
902 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 ...
237 views

### Minesweeper challenge #4

While solving another Minesweeper puzzle, I ran into yet another unsolvable corner. Well, actually, this time I have two unsolvable corners in the same puzzle. Here's the bottom left corner: ...as ...
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 ...
80 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 ...
304 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 ...
208 views

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 ...
193 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'...
232 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 ...
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 ...
3k views

### How can the “Boy or Girl” paradox be worded unambiguously?

The first time I encountered the Boy or Girl paradox I was struck by how ambiguous all of the formulations in English are. As Wikipedia notes: Gardner argued that a "failure to specify the ...
830 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 ...
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 ...
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 ...
207 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 ...
78 views

### Place Your Bets 3 , last of the series

A harder sequence to figure out... What are the next 4 cards, including suits?
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
906 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 ...
285 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 ...
2k views

### Hamlet and the theatre

Hamlet is preparing a play to find out the truth about his father's death. The theatre has $2015$ numbered seats and can contain all the members of King Claudius's court. He gives to each member a ...
5k views

### Do better than chance

You and an opponent are playing the following game: Your opponent picks two different real numbers, however he wants to, and writes them on two cards, which he presents to you face down You choose ...
1k views

### A first choice die

You and your friend have met to play a game of dice. This is a very simple game where both players roll a die at the same time, and the player with the lower score pays a coin to the other player. In ...
2k views

### Birthdays on Consecutive Days

You are allowed to select as many random1 people as you like, and place them in a room. How many do you need for the probability that at least 2 people will have a birthday2...   a. on the ...
1k views