# Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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### 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 ...
4k views

### The “M&M Sugar Rush” game

Suppose I have in my possession a incredibly large (almost infinitely large!) bag of M&Ms containing a uniform distribution of the 6 M&M colors. I'm bored, so I decide to play a game: I draw ...
1k views

### Picking a time to bet

You play a game with a friend: he deals cards face up one a time from a uniformly shuffled deck of 26 black cards and 26 red cards. At some point before all the cards have been dealt, you must call "...
2k views

### Digging a tunnel between random locations

Romeo and Juliet are each placed uniformly at random locations on a spherical planet, meaning that each square meter of surface area of the planet is equally likely. Romeo decides to dig a straight-...
608 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 ...
1k views

### Coins, Dice, and Probability! [closed]

Background: It's time for a little bit of fun, your friends are playing a game and you decide to join them! Gamplay: You each sit down and play on a flat surface. You sit in a circle and each throw ...
1k views

### Another probabilistic coin puzzle

Credit to GOTO0 for the original idea for this puzzle, which is the converse of his puzzle. In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, ...
6k views

### Left coin, right coin, last coin?

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 them on the table in front of them. Then each ...
14k views

### Does the drunk man fall off the cliff? (a random walk problem)

A drunk man stands with a cliff one step to his left. He takes steps randomly left and right. Each step has probability $p$ of going left and probability $q=1-p$ of going right. Each step is the same ...
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 ...
3k views

### Multiple Choice Puzzle

What are the chances of getting this correct if you pick at random? 1/4 1/2 1/3 1/4 You are not allowed to add more answers to this list Note; This DOES have a correct, demonstrable answer!
2k views

### 100 chocolate bars! [duplicate]

A boy was taken to a magical land of wonder and chocolate, but sadly, a disease broke out in this land! He has to face off the evil Dr. Vanscosh, who caused the disease to break out, in a probability ...
565 views

### Trick-Or-Treat Probability Puzzle [closed]

On Halloween night, a young boy was trick-or-treating. It was late at night and he was on his last stop. He knocked at the door and said: Trick-or-Treat! The man inside said he had a bag of just 4 ...
2k views

### Random Walk on Ring City

Ring City has 100 houses arranged in a circle. Alice starts at her own house, and every day she randomly moves to one of the two adjacent houses, each with 50% probability. She repeats this until she ...
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 ...
328 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 ...
3k views

### A Strangely Familiar Probability Problem

You're taking the final exam for your Introduction to Probability and Statistics course, and once again you've failed to study (you were up all night solving online brainteasers). The exam is ...
978 views

### Social Engineering (The Birthrate Problem)

The distant country of Toomalia has a birthrate of 67 boys for every 33 girls. In an effort to restore a 50:50 gender ratio in the country, Toomalian policymakers institute a mandatory new social ...
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 ...
4k views

### Is my sibling a sister [duplicate]

A male friend of yours wants to test if you are ok at Math and logical thinking, he says I am one of two children of my parents, and asks you to find out the probability that his sibling is a sister, ...
7k views

### Flip a Fair Coin

I found this question and became curious, can anyone tell me the answer and prove it, i know it seems fairly simple but just thought an explanation of this would make an interesting case. Flip a fair ...
485 views

### The 3 Boxes Show! [duplicate]

A variation of the Monty Hall, where the values inside the choices are changed You were just out gambling and lost 5000 dollars! Of course being the gambler that you are, you pay 2500 to play this ...
1k views

### Do you choose the other door? [duplicate]

You are on the final round of a TV gameshow, there are 3 doors; A, B and C. Two doors lead to a goat and the other door leads to a sports car. In each episode the presenter asks the contestant to ...
854 views

### 100 sequential parking spaces

I just came up across this question in the mathematics stack exchange site and found it quite interesting: 100 autonomous robotic vehicles enter a warehouse in random order to park. Inside the ...
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 ...
2k views

### Two Card Probability Problem

I came across this puzzle somewhere on the interwebs. Has stumped me for an answer for quite sometime. Helpplease? Someone picks, at their will, two cards from a deck of cards. The cards have ...
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 ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. ...
2k views

### Entangled physicists

The anti-intellectuals have won the war, and under the iron rule of emperor Nonotin anyone who has been deemed too smart for their own good has been brought to labour camps. But most of the science ...
3k views

### The Monty Hall problem

I'm amazed that, although well known, this problem hasn't been posted yet. Monty Hall You are on a game show. The host of the show shows you three doors. He tells you that behind one of them, is a ...
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, ...
554 views