Questions tagged [probability]
A mathematical puzzle whose essential nature involves randomness.
3
votes
0answers
169 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 ...
17
votes
6answers
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
132 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
267 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
594 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
102 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
84 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
184 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
153 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
68 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
188 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
330 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
332 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
131 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
104 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
220 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
423 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
389 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
205 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
469 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
217 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
607 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
486 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
448 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
555 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
160 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 ...
40
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 ...
6
votes
3answers
343 views
Guessing game with infinity coin flips
Evan and Ollie are going to play a game as a team. The two friends placed in separate rooms, and then a coin is flipped infinitely many times*. Evan is told the results of the even numbered flips, ...
5
votes
1answer
233 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 ...
0
votes
1answer
79 views
Taking a ball from basket challenge [duplicate]
I have 10 red balls, 10 blue balls, and 2 baskets.
You are free to choose the numbers of red balls, and the numbers of blue balls to put to the first basket.
Then you have to put rest of the balls to ...
6
votes
2answers
748 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 ...
2
votes
2answers
302 views
A Shooting Target with 9 shots
You are a soldier in the army, and the commander is testing his soldiers for their shots. But the commander is also a mathematician and would like to test not only your shooting ability but also your ...
7
votes
2answers
2k views
Find Coin's unfairness with only 4 tosses
There is a unfair coin and you want to find out its actual probability, to find the exact probability is actually not an easy task, you need to toss it many many times to get the close to actual ...
10
votes
7answers
969 views
Prisoners and minority voting
Disclaimer: this is a scenario that I came up with on my own, and I do not actually know if there is a possible solution. The reason for posting is to see if the combined intellect of PSE can help to ...
6
votes
2answers
596 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)...
3
votes
2answers
344 views
The most probable key
You broke into John Doe's house and found the safe. It has a combination lock with 4 dials ranging from 0 to 9 each. ...
-3
votes
5answers
224 views
Interesting card combinations [closed]
In a normal pack of playing cards (without jokers), the probabilities of the following events are the same:
(1) Drawing a set of 4 different cards (irrespective of its color and suit) - let us call ...
2
votes
1answer
156 views
Dice problem involving nine randomly selected cups [closed]
I was given this problem by a colleague, and I cannot figure it out.
Given nine cups and an unlimited supply of six-sided dice rolled one at a time, what is the probability that you will, at some ...
8
votes
2answers
519 views
Help! I lost my marble(s)!
Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The days festivities will include various marble games, admiring collections of marbles, a guest speaker who will talk ...
22
votes
3answers
4k views
bored of eating soup
A man orders spicy noodle and leek soup from a restaurant, but gets bored while eating.
When he gets bored, there are exactly 100 noodles in the soup. Because he is bored, he decides to play a game ...
4
votes
3answers
580 views
Effective strategy for prisoners to see movie
100 prisoners are given an opportunity to go to a theatre and watch a movie. Each can choose either to go or not. However, if everyone chooses to go to the trip then no one is allowed to go.
The ...
