Tagged Questions
3
votes
2answers
57 views
Probability in Minesweeper
Suppose I click a random tile during a Minesweeper game. It is a 1. During each time I click an adjacent square, what are the chances of hitting a mine? How would this change if it were a 2 or another ...
4
votes
0answers
67 views
Colored balls puzzle
Imagine you have $n$ balls in a bag that are colored from $1$ to $n$. At each turn you take two balls at random out that have different colors and color one the color of the other. You then put them ...
2
votes
1answer
145 views
Another hat problem
A finite number of prisoners, after being given their hats (black or white), are able to see one another but themselves, and then they are ordered to jot down their guess on the color of their own ...
1
vote
1answer
48 views
On the arrangement of digits on a dice
In a cubic dice, the sum of the numbers on 2 opposite faces is 7, why are numbers arranged in such a way? Would the result of throwing a dice (1 or more times) still yield a random number if the ...
1
vote
2answers
147 views
Weather station brain teaser
I am living in a world where tomorrow will either rain or not rain. There are two independent weather stations (A,B) that can predict the chance of raining tomorrow with equal probability 3/5. They ...
5
votes
2answers
67 views
100-sided die probability
The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the ...
3
votes
2answers
47 views
What to bid for this treasure chest? (puzzle)
Suppose you are given the opportunity to bid for a treasure chest, which you know to be priced anywhere between 0-1000 dollars inclusive). Treasure price is uniformly distributed. If you bid equal to ...
0
votes
1answer
47 views
A word problem concerning probability. Its pretty interesting
I found an interesting word problem. Check out this link:
http://www.math.hmc.edu/~ajb/PCMI/pcmi12.pdf
It is problem $A7$. I have been working on it and have reached the following conclusion: Say ...
3
votes
1answer
93 views
Safes and keys probability puzzle [duplicate]
I have $100$ keys and $100$ safes. Each key opens only one safe, and each safe is opened only by one key. Every safe contains a random key. 98 of these safes are locked. What's the probability that I ...
2
votes
2answers
174 views
Probability Question relating prison break
I am stuck in a question regarding a prisoner trapped in a cell with 3 doors that actually has a probability associated with each door chosen(say $.5$ for door $A$, $.3$ for door $B$ and $.2$ for door ...
1
vote
2answers
99 views
Interesting and irritating problem.
How to deal this problem. I found this problem in math competation in 2012. But, I could not solve. Could you help me...
Uncle John has taken blood pressure drops for a long time according to the ...
1
vote
2answers
71 views
Easy Probability Problem
I was told the following probability problem:
While doing a math problem today at the contest the probability of Annie, Tom and Karen getting
the problem correct first is 1/7, 1/2, and 5/14 ...
2
votes
1answer
100 views
Monty Hall Application
Driver A comes to a 3 way path junction but is not sure which one to take.
Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would ...
1
vote
3answers
101 views
Monty Hall problem vs. roulette systems - how are they different?
So I got interested in the Monty Hall problem - I understand what it's about, but somehow I can't wrap my head around the idea of the final choice not being 50/50. More precisely: we all know (or ...
2
votes
2answers
71 views
Puzzle on Ranks
Here is a puzzle from textbook : 40 Puzzles and Problems in Probability and Mathematical Statistics
Peter draws n = 100 independent realizations of a continuous rv and ranks them in increasing order ...
1
vote
2answers
136 views
Mystery card probability riddle [duplicate]
Possible Duplicate:
The Monty Hall problem
I’m looking for the better explanation to the solution of this riddle, because I always struggle to get people to accept the ones I know.
Riddle:
...
1
vote
4answers
378 views
Selection through identical balls
I was trying the following puzzle from this link :
You randomly withdraw 3 balls out of a lot containing identical red, identical green and identical blue balls. What is the probability that you get ...
0
votes
1answer
152 views
Puzzle: Guessing the bigger number!
Consider the following interesting puzzle:
"Alice writes two distinct real numbers between 0 and 1 on two sheets of paper. Bob selects one of the sheets randomly to inspect it. He then has to ...
4
votes
2answers
125 views
Bidding Item Problem
You are bidding on an item that has an unknown value uniformly
distributed between 0 and 1. You do not know the true value of the
item, but you know that if you end up winning the bid for the ...
0
votes
1answer
255 views
Approximating Coins Flips Problem
Approximate the probability of getting 500 heads out of a 1000 coin
flip of unbiased coins to be within 5% of its true value (without the use of a calculator).
I know that an exact probability ...
2
votes
2answers
119 views
Name Drawing Puzzle
There is a party with 20 people, and everyone writes their name down
on a piece of paper and puts it into a bag. The bag is mixed up, and
each person draws one piece of paper. If you draw the ...
3
votes
1answer
147 views
Opening Doors Puzzle
You are in a corridor which has N doors all of the doors are opened.
Every time someone passes through the corridor, he closes randomly
with equal probability a certain number of doors between ...
1
vote
2answers
80 views
estimating a person's daily rotations
I ran into this question at an interview recently. The idea is more to think out loud and work out some reasonable estimates than anything else.
The question is: how many times does an average ...
3
votes
2answers
330 views
Flipping Cards Probability
You have a deck of cards, 26 red, 26 black. These are turned over,
and at any point you may stop and exclaim "The next card is red.". If
the next card is red you win £10.
What's the ...
6
votes
1answer
241 views
Nice riddle - is there an elegant solution [duplicate]
Possible Duplicate:
Taking Seats on a Plane
There are 100 seats on a plane and 100 passengers, each with his ticket. However, the first person to enter the plane discovers he has lost his ...
1
vote
1answer
194 views
Probability puzzle with balls in an urn
I need help with a problem about classic probability and possible extensions to it. Suppose you have an urn with $N$ distinguishable balls. Every time you draw $k$ balls out of $N$. Some possible ...
0
votes
2answers
374 views
Circular Permutation Problem
We play Russian Roulette. There are 4 blanks 2 bullets (assuming you randomly pick 2 places the bullets can go in the cycle, then spin it randomizing the how the rotation ends up). If someone
...
2
votes
1answer
334 views
Expected Value of the Difference between 2 Dice
What is the expected value of the absolute difference between 2 N
faced dice? What about the difference between 2 dice one with N faces
and one with M faces?
While finding the expected value ...
6
votes
1answer
389 views
Improving Von Neumann's Unfair Coin Solution
If a cheat has altered a coin to prefer one side over another (a
biased coin), the coin can still be used for fair results by changing
the game slightly. John von Neumann gave the following
...
9
votes
2answers
776 views
100 prisoners and a lightbulb
100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb ...
8
votes
2answers
423 views
A riddle about guessing hat colours (which is not among the commonly known ones)
This is a riddle I heard recently, and my question is if someone happens to know the solution. I'm asking this out of curiosity more than anything else.
So here it is. The riddle is one of the ...
2
votes
3answers
314 views
Two ants on a triangle puzzle
Last Saturday's Guardian newspaper contained the following puzzle:
Two soldier ants start on different vertices of an equilateral triangle. With each move, each ant moves independently and ...
-5
votes
1answer
197 views
King of Spades puzzle [closed]
There are on the table 3 playing cards face-down. You have to guess which one is a King of Spades. You pointed the card C... OK, card B is turned over by our game Host and it isn’t a King of Spades. ...
33
votes
6answers
1k views
A variant of the Monty Hall problem
Everybody knows the famous Monty Hall problem; way too much ink has been spilled over it already. Let's take it as a given and consider the following variant of the problem that I thought up this ...
-2
votes
1answer
286 views
One drunk receptionist and four brilliant mathematicians
Suppose that there is one hotel with nine floors (first floor = ground floor + 1) where the math seminar takes place, four brilliant mathematicians who are guests of the hotel, one drunk receptionist
...
5
votes
4answers
835 views
Better than random
I have been trying to solve this question, but in vain. Please help.
You are given two boxes with a number inside each box. The two numbers
are different but you have no idea what they are. You ...
0
votes
1answer
150 views
Is the average of many “random” numbers useful information?
Ok, so I found this site: http://tweetcracker.com/. Essentially, people just tweet 10 digit numbers in hopes it is the correct number (like lottery, except free).
I heard that if you took all the ...
2
votes
1answer
98 views
Preferences Paradox [duplicate]
Possible Duplicate:
Card doubling paradox
I came across the following preferences paradox:
Suppose you have two identical boxes $A$ and $B$. One of them contains an unspecified number ...
10
votes
5answers
604 views
Four men, hats and probability
I encountered the four men in hats puzzle for the first time today. My question is about a realisation I (think I) had while arriving at the solution, but I have no idea whether I've made a mistake ...
3
votes
3answers
278 views
grid puzzle about combinatorics
Here is a puzzle about combinatorics.
Suppose you have a square grid with $n^2$ points. You want to go from the origin $(0, 0)$ to $(n-1, n-1)$. Assuming you can only go right or up, in how many ways ...
2
votes
2answers
625 views
Variation on the Monty Hall Problem
Many of us know the [Monty Hall Problem][1]
But the other day I was asked a variation of this riddle.
The answer of the original question is, of course, $ 66\% $ in favor of changing doors, but this ...
2
votes
2answers
243 views
Probability of an expected outcome
I'm in a class titled "Puzzle Based Learning" and we were given this problem:
There is a new game show and you are
the participant. There are two doors,
each has a suitcase with gold coins
...
2
votes
3answers
209 views
Maximise conditional probability of urns
I have two urns, urn $1$ contains $k$ white balls and $l$ red balls, urn $2$ contains $n - k$ white balls and $n -l$ red balls. I have the total probability
$ P($ "white ball is drawn" $) = ...
27
votes
5answers
6k views
Chance of getting a date
A girl you like tells you that there's a 1% chance she'll go out on a date with you. What is the expected number of times you have to ask her out before you get a date?
(Not a homework problem - I ...
4
votes
2answers
191 views
Particle moving at constant speed with Poisson setbacks
Consider a particle starting at the the origin and moving along the positive real line at a constant speed of 1. Suppose there is a counter which clicks at random time intervals following the ...
11
votes
3answers
642 views
Covering ten dots on a table with ten equal-sized coins: explanation of proof
Note: This question has been posted on StackOverflow. I have moved it here because:
I am curious about the answer
The OP has not shown any interest in moving it himself
In the Communications of ...
