Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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votes
4answers
768 views

Born to lie, to live, to die

There is a race which has a truth gene. It consists of 3 alleles, namely T, F and O. A person inherits one allele from each of his parents, hence he/she has always exactly two alleles. For example, if ...
7
votes
1answer
169 views

Guessing the coin flips [duplicate]

Two prisoners, Alice and Bob, are captured by a dragon and placed in separate, isolated cells. The dragon then flips an infinite number of fair coins, and tells the outcomes of odd throws to Alice and ...
7
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3answers
173 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 ...
7
votes
1answer
166 views

The Attack on Fort Alpha

I made this puzzle up in 1999 when I was a student. Fort Alpha, on your border territories, was attacked by The Enemy. You don't know if it fell, or repulsed The Enemy's vicious onslaught. A totally ...
7
votes
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 ...
7
votes
3answers
447 views

Two Dragons and a Princess

The Quest You are a knight tasked with rescuing the King's daughter. The princess is being held captive by a band of evil dragon pirate monks. You've been debriefed with prior intelligence gathered ...
6
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5answers
3k views

A chess board and a coin! [closed]

You have a standard chessboard, consisting of $64$ squares ($32$ white and $32$ black) each of dimensions $4\times4$ cm, and you have a standard coin of $2$ cm diameter with tail and head. You flip ...
6
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5answers
1k views

Probability of three identical digits on a four-digit digital clock?

On a digital clock showing 00:00 to 23:59, what is the probability of having exactly three identical digits?
6
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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 ...
6
votes
5answers
2k views

Ten targets you need to hit

You are a good sniper and there are 10 targets you need to hit. The chance of hitting any target is the same. Strangely, with your accuracy the chance of getting 8 hits is equal to getting 7 hits in ...
6
votes
4answers
1k views

A bet with your friend

James, your friend, has invited you to bet with him. He has a fair die, with $3$ faces showing $0$ and $3$ faces showing $1$. You pay him $\\\$70$. He throws the die $15$ times, and records the sum of ...
6
votes
2answers
781 views

Drawing balls from a pocket

I have a pocket of N=4 balls of different colors, say green, red, blue and yellow. You can draw as many times as you want After each draw, the ball will be put back to the pocket so that the chance ...
6
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7answers
7k 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. ...
6
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2answers
735 views

A book with only two letters

Dr. G somehow detests reading novels but he decided to read a one then he naturally got bored and decided to delete all letters except A and B letters in the book. So with this new book which ...
6
votes
2answers
797 views

Exam statistics

250 teenagers gather for an exam. Peeking at the roll, a math-inclined among them note that if they are split into 10 groups of 25 per alphabetical order, then in each group, there are two with the ...
6
votes
4answers
385 views

Drawing uniformly using a single biased coin

Your task is to draw uniformly from a set of size $N$. You are given a single coin which you can ‘bend’ to control the probability $p\in[0,1]$ of throwing a Head, but you are only allowed a bounded ...
6
votes
5answers
2k views

How to maximize your wages?

You're trying to work out how to maximize the wages you receive in the month of February (in a non-leap year). You must work at least 5 days a week and at least 5 hours a day, but you can also work on ...
6
votes
2answers
321 views

More coin flipping

After their last game, Alice and Bob decide to have a bit more fun with their fair coin. Bob proposes the following game: considering a flip can come out as heads or tails, they will both predict one ...
6
votes
1answer
1k views

cheating on the Russian roulette

This question is inspired by this one. You and your opponent play Russian roulette with two bullets. Quoting from the linked question: You are challenged to a game of Russian roulette. Your ...
6
votes
3answers
630 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 ...
6
votes
2answers
672 views

A jar of mixed coins [closed]

This is a slight adaptation of a google interview question that I found entertaining. You are given a jar with N coins, K of them are fair. The remaining coins have heads on both sides. You choose a ...
6
votes
1answer
322 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 ...
6
votes
2answers
663 views

Probability of nobody being born in a specific month

Assume 11 persons are born in 11 different months. What is the probability $P(n)$ that none of them is born in the $n$-th month? This would be pretty easy if all months had the same length, then $P(n)...
6
votes
3answers
354 views

Intersecting bug trail [closed]

A man picks up a huge circular dart board and shoots paintballs at it. $n$ paintballs manage to hit it. They are random and point-sized, for the purpose of this question. A bug is somewhere on the ...
6
votes
1answer
659 views

What is the expected length of the longest piece?

If a rod of unit length is broken into $n$ pieces, what is the expected length of the longest piece? The positions at which the rod is broken are chosen randomly uniformly. This is a generalization ...
6
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2answers
406 views

Jewels in the box

Professor Egghead participates today in a local game show. There are six jewels (a diamond, an emerald, a moonstone, a ruby, a sapphire, and a topaz), and there are six boxes that carry the numbers 1,...
6
votes
1answer
209 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
412 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
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2answers
795 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 ...
6
votes
1answer
145 views

Darwin Fooling Dalton

Dalton wants to measure the effectiveness of a treatment for a particular type of plant and, being a good scientist, decides to have a control group that does not have the treatment. He is able to ...
6
votes
2answers
256 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, ...
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 ...
5
votes
5answers
463 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
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
2answers
855 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
6answers
412 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
4answers
342 views

A probably sunny Sunday

Besides this problem I also use the following one to rise the interest of my students on the Probabilities Theory. It's a funny puzzle were the use of simple arithmetic rules doesn't work. We have to ...
5
votes
2answers
846 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
365 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
1k 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
579 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
1k 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 in ...
5
votes
1answer
120 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
1answer
243 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
3answers
531 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
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 ...
5
votes
2answers
223 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
2answers
250 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 ...
5
votes
3answers
214 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'...

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