# Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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1answer
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### Lap Theory Optimal Betting Game

Three prisoners are seated at a table. Each of them has a mobile phone on their lap, and they are not allowed to look at anyone else’s phone (and obviously no other form of communication is allowed). ...
2answers
334 views

### Three way duel, which guns to choose?

Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
5answers
513 views

### Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
1answer
823 views

### Lawbreaking by the numbers

Special Agent Benford has been stymied by a third unsolved case of miscreant creative accounting and will voluntarily retire from the Fraudulent Numbers Task Force. Benford’s ability to detect ...
5answers
937 views

### Two player Monty Hall variation

Alice and Bob are going on a game show as partners. In this game, there are three doors, which contain a car, the car keys, and a goat, which are arranged randomly and secretly behind the doors. Alice ...
4answers
1k views

2answers
153 views

### Cheapest strategy on average to find specific items in a set

The problem You have a set on N (around 15-30) seemingly-identical objects, which in fact comprises a small number D (unknown, between 1-3) of defective objects and the rest (N-D) are good. There is a ...
0answers
54 views

### A Dices Probability Riddle [duplicate]

Bob (A), Steven (B) and Joe (C) were playing with dices, each one of them made his own dice and wrote a number between 1-6 on each side of his dice. After playing for a while they've noticed that : (...
0answers
99 views

### full unmatch probability [closed]

You have 5 distinct color envelops and 5 distinct color letters. You randomly put one letter in each envelop. What is the probability of no pair matching in color? I can find the answer with brute ...
1answer
313 views

### Frog in the Well [duplicate]

A frog is trapped in a well, just 1 meter below the lip. On sunny days, the well is dry, and the frog is able to climb up 1 meter. On rainy days, the well is wet and the frog slides down 1 meter. If ...
1answer
155 views

### Not a coincidence

Your company has successfully made 140 sales since they started promoting the new product. The other owner, who is very superstitious, notices that today is the 140th day of the year, and believes ...
2answers
248 views

### Achieve the best outcome by a tactical statement

This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
0answers
110 views

### Probabilities for “What number is that? — asks grandpa”

Inspired from Multilanguage generalization of "What number is that? Asks Grandpa" and What number is that ? Asks Grandpa In this puzzle we will use the English alphabet of 26 letters. We ...
1answer
97 views

### Ideal number of Fruit Baskets

I'm not sure if this is more of a Math or a Puzzling question, but I'll give it a shot here due to it's game related aspects and rules. I've been playing some Runescape lately and while training the "...
1answer
202 views

### The sadistic chieftain and the lethal truel game

In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind. "I'll ...
5answers
335 views

### Find the optimal strategy for this dice game

You are playing a game: You have $6$ standard 6-sided dice that are all rolled at the start of the game. The sum of dice values is your score. Each turn, you can take any (or none) dice and reroll ...
3answers
663 views

1answer
261 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 ...
3answers
204 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 ...