Questions tagged [probability]
A mathematical puzzle whose essential nature involves randomness.
12
votes
11answers
4k 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
188 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 ...
40
votes
11answers
8k views
3 doors, three guards, one stone
You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want ...
16
votes
5answers
650 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 ...
15
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
1answer
729 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
1answer
136 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 ...
5
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
78 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
99 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
353 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
163 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
197 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
2k 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
141 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
420 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
625 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
91 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
9k 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 ...
0
votes
1answer
120 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 ...
1
vote
1answer
97 views
Minesweeper challenge #3
I seem to have run into yet another "unsolvable corner" while playing Minesweeper.
The following segment is taken from the bottom right corner of the puzzle. There are 5 mines remaining, and all ...
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 ...
4
votes
2answers
201 views
Minesweeper challenge #2
Again, I seem to have run into another situation where there doesn't seem to be a definitive set of squares to tap to solve a Minesweeper puzzle.
What squares should I tap to maximize my chances of ...
3
votes
2answers
185 views
Is there a definite answer to this Minesweeper puzzle? If not, which square has the best chance of being safe?
I was working on solving an Expert puzzle in Minesweeper, but came across a hurdle in this corner (the top left).
Is there a definitive solution to the problem? If so, what is it? If not, which ...
-3
votes
1answer
93 views
max possible number of dice throw [closed]
Scott repeatedly rolls a pair of standard six-sided dice and keeps track of the
sum of the two numbers rolled each time. So far he has not rolled any sum
twice. What is the maximum possible number of ...
6
votes
1answer
192 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 $20$ ...
12
votes
3answers
341 views
Guffin factory regulated heist
I work at a guffin factory. I manufacture guffins and have an unlimited access to guffin storage. I can fit up to 20 guffins in my bag, get them home from the factory and nobody will chase me.
You ...
4
votes
6answers
5k views
100 pieces 1 opportunity, choose wisely!
Say you have a cake that is cut into 100 pieces.
One of the pieces has a hidden prize.
100 people take turns, each taking a piece in sequence hoping to find the prize.
Note: I slightly modified (...
5
votes
3answers
340 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”....
4
votes
2answers
135 views
3 points on a circle [duplicate]
There is a circle where you put 3 points randomly on it as shown below:
What is the chance of these randomly chosen three points passing on an half circle?
Reference: Bilim Teknik Dergisi 2018-07
13
votes
4answers
3k views
A dice game, what is the optimal strategy?
Alice was walking on the street when she came across a man playing with a die. She could not help trying to check if the die was loaded and while she was concluding that it wasn't loaded, the man ...
3
votes
0answers
108 views
Variation of Boy/Girl Birth Problem [closed]
Parents keep having children until they have one girl, at which point they stop; and babies are girls with probability 0.49.
If we select a child uniformly at random (from the entire population of ...
4
votes
1answer
225 views
How likely is a comeback in basketball?
For this most recent NBA season, ESPN.com has had in-game win probabilities:
My question:
Say a team gets a big lead and has a 90% chance of winning. What is the probability that at some point ...
10
votes
7answers
444 views
A cooperative guessing game - Guess your order and card
6 players sitting in a circle and each assigned a card among 2 Hearts, 3 Hearts, ..., Ace Hearts (i.e. any of the Hearts cards). Holding her card above his forehead (i.e. Indian Poker fashion), each ...
8
votes
5answers
396 views
Two person game, choosing an integer between 1 and 30?
Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
1
vote
2answers
221 views
What are the chances on watching the clock? [closed]
This is a relatively straightforward little puzzle, but the answers are somewhat unintuitive or can prompt a new perspective. It might be an interesting little puzzle for a probability teaching ...
5
votes
3answers
484 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 ...
-4
votes
2answers
228 views
Random chord to a circle around a triangle
This puzzle is literally a math textbook question. Its only redeeming feature is that it also happens to be too broad in a surprisingly interesting way.
The problem
Given the circle $\mathbf O$ ...
31
votes
7answers
5k views
Monty Hall Revisited: Winning Both Goats!
Suppose you're at a game show, knowing the winning strategy for the classic Monty Hall problem. Your turn comes up and you take the stage. You confidently choose door number (?).
Just as you are ...
11
votes
2answers
789 views
Expected Number of Tosses Until H,T,T,H
I found a nice little app/game the other day called Probability Puzzles. Apologies to those who, like me, will now obsess until they are all completed. I'm sure there will be many such people on this ...
8
votes
2answers
1k views
Keypad Door Lock
Your progress is barred by a locked door, it is clearly controlled by a keypad. with 10 digits (0-9) plus a button for ENTER and a button for CANCEL. You know several things about this lock:
This ...
4
votes
3answers
507 views
Lottery in Minesweeper
The question is inspired by this scenario:
In this case, we had 2 tiles remaining, and each had the equal probability of being a mine, based on the already deduced information. Thus it was necessary ...
15
votes
2answers
474 views
“Musical chair” for clock hands
A colleague and me usually make bets on the time when a simulation is finished. Next time I would suggest the following: At the time the simulation is finished we take a look at the analog clock on ...
9
votes
2answers
580 views
What is the probability that all the bullets will be destroyed?
A gun shots bullets with different speed each second.
The bullets form a straight line.
The bullets keep their speed (not getting slower or faster).
But if 2 of the bullets collide, 2 of them are ...
1
vote
2answers
161 views
Landing 4 on a Broken Die [closed]
This is not hard, but fun.
Suppose you have a die such that its 1,5,6 and 4 face are broken. Whenever 1 face lands, it gets rolled over to an adjacent face. If 5 face lands, it is equally likely that ...
41
votes
7answers
8k views
How many tries to roll a 6?
Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6.
Now ...
