# Tagged Questions

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### Non-geometric way to calculate expected value of breaks?

In "50 Challenging Problems in Probability", question #43 is the following: "A bar is broken at random in two places. Find the average size of the smallest, of the middle-sized, and of the largest ...
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### Puzzle about technique of fair using of unfair coin

There is an unfair coin. It tends to land on one side more than on the other. It is unknown which side is it. There is Mr. A and Mr. B. They argue about something and they want to use that coin to ...
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### Russian roulette should a player pull the trigger or spin the cylinder

Two men plays Russian roulette. In revolver there are 2 bullets in consecutive chambers( 2 bullets are in 2 chambers next to each other). One man spun the cylinder, pulled the trigger and he is fine, ...
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### Drawing previously undrawn cards from a deck

Suppose you have a deck of $y$ cards. First, randomly select $y-x$ distinct cards and sign the face of each, then shuffle all the cards back in to the deck. Proceed as follows: Draw a card. If it is ...
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### Probability: A variant of the Monty Hall Problem

Monty has a new game it's like his old one but now there are no goats just one car hiding behind one of three doors and this time he doesn't know where the car is. To play you pick one of the three ...
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### Two children paradox : where is my reasoning wrong?

I hope here is the good place to be asking this. Apologies otherwise. The statement is as follow : "Ms Michu has two children. We know one of the two is a girl, we call that girl Ludivine. What is ...
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### Probability Puzzle: Mutating Loaded Die

Take an (initially) fair six-sided die (i.e. $P(x)=\frac{1}{6}$ for $x=1,…,6$) and roll it repeatedly. After each roll, the die becomes loaded for the next roll depending on the number $y$ that was ...
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### game theoretic die rolls

Suppose player X has a 6 sided die and player Y has a 10 sided die. They each get two rolls and they can each choose to stop rolling on either one of the rolls, taking the number on that roll. Whoever ...
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### expected value of a game with a n sided die

Suppose we have a n-sided die. When we roll it, we can be paid the outcome or we can choose to re-roll by paying $1/n$. What is the best strategy and what is the expected value of this game? As an ...
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### Puzzle about probability of colour of a billiard ball left in a bag

A bag contains one billiard ball. It can be white or black (with equal probability). We put a white ball inside the bag (so now there are 2 balls in the bag). Now we take one ball from the bag. It ...
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### hitting a dart board probability

You have a dart board which is split in half. If you hit the left half, you get $2$ points, if you hit the right half, you get $3$ points. You have an 80% chance of hitting the dart board on any ...
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### Random permutation with a scientific calculator

I have 8 people whom I want to divide into 2 groups. The allocation must be uniformly at random, i.e., every person must have equal probability of joining either group. We came across a situation ...
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### expected value of a sum of a 10 sided die

Suppose you have a fair die with 10 sides with numbers from 1 to 10. You roll the die and take the sum until the sum is greater than 100. What is the expected value of this sum?
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### Making a biased coin flip fair

I have a puzzle: Two groups want to break a tied vote using a simple coin flip, however the only coin they have available is a biased coin (i.e., one side will come up more often than the ...
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### Would you please take a look if my substantiation is correct?

The four numbers 4, 5, 6, 7 are randomly inserted into 7 .3 .4 . 6 . 48 The result is a ten-digit number - for example, 7 4 3 5 4 6 6 7 48 How high is the chance, that the number created is ...
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### Probability that a leap year has 52 Sundays

For the Question "Find the probability that a leap year has 53 Sundays". The Solution goes : For 53 Sundays, we proceed as: $\frac{366}{7} = 52.28$; So we can be sure that there are 52 Sundays, ...
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### Generating functions and the blue eyed daughters

There is a famous problem, given that a man has a number of daughters and if you were to meet two of them at random there is a 50% chance that both have blue eyes. How many daughters does the man ...
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### Stuffing envelopes

I've been trying to solve a following riddle A secretary types four letters to four people and addresses the four envelopes. If she inserts the letters at random, each in a different envelope, ...
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### Sudoku candidate probability

Supose a Sudoku puzzle row has four empty cells. The candidates for each cells is as follows: $3, 6, 9$ $7, 9$ $3, 6, 7$ $3, 7$ Looking at the possible cells for $3$ (cells $1$, $3$ and ...
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### Is Lewis Carroll's reasoning correct?

A bag contains 2 counters, as to which nothing is known except that each is either black or white. Ascertain their colours without taking them out of the bag. Carroll's solution: One is black, and ...
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### Fisherman riddle: Combining probabilities

This is more a probabilities problem than a riddle. The riddle is: I am in a village, where a fisherman lives. The fisherman tells me that there is a 70% possibility that it will rain tomorrow. I ...
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### A three-way duel (probability puzzle)

This puzzle is taken from Mathematical Puzzles: A Connoisseur's Collection [Peter Winkler]. I don't understand the solution. Alice, Bob, and Carol arrange a three-way duel. Alice is a poor shot, ...
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### To maximise my chance of winning one prize should I put all my entries in a single draw?

Every week there's a prize draw. It's free to enter using the code from a soup tin lid. You can enter as many times as you like during the week until Monday's draw and then it starts all over. The ...
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### 3 trams are coming every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come?

3 trams are coming to the stop every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come? It's a practical problem, not some kind of a riddle for which I have a ...
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### Puzzle of Probability Can give an idea …

A bird keeper has got $P$ pigeon, $M$ mynas and $S$ sparrows. The keeper goes for lunch leaving his assistant to watch the birds. Suppose $p=10, m=5, s=8$. When the bird keeper comes ...
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### probability of a word in a string

What is the probability of a word n characters long appearing in a string of m characters, in an alphabet of x characters? A word here is simply a string of characters contained in another string of ...
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### Puzzle - zero knowledge proof

I am solving the following problem : I have edge-matching puzzles, where all pieces are squares and the grid has $n$*$n$ format. There is no global image to guide a puzzle solver. Despite the puzzles ...
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### How many combinations can be made in the game Sudoku [duplicate]

I have the game Sudoku. how many combinations can be made by random entering of numbers on the whole such that it makes unique combination in $3\times 3$ grid and $9\times 9$ also.
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### Probabilistic puzzle

There are $n+1$ boxes and every box contains $n$ balls. For every $k\in\left\{ 0,1,\ldots,n\right\}$ there is exactly $1$ box containing $k$ white balls and $n-k$ black balls. A box is picked out and ...
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### A new variation of the Monty Hall problem

Everybody knows the famous Monty Hall problem http://en.wikipedia.org/wiki/Monty_Hall_problem I will try again and I am sorry if I was not clear enough but please understand that I am here and asking ...
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### Probabilistic riddle

If you choose an answer to this question at random, then what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25% On internet you can find the problem here.
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### A fly on a triangle?

A fly is on the vertex of a triangle. It can move left with probability $\frac 12$ and right with probability $\frac 12$. What is the expected number of moves till it reaches its starting point? ...
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### Calculating that confidence that pairs of lightbulbs are independently illuminated.

So, you're sitting in a dark room, and on the far wall you see $n$ lightbulbs mounted above plaques numbered $1$ through $n$. There is a lightswitch on the arm of your chair. Every time you flip the ...
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### probability that broken sticks will not form a triangle.

A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio 4:3. What is the probability that the three ...
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### Dice probability puzzle

What is the probability of a run of at least 3 sixes when a die is thrown 5 times? I think I have the answer but from what I have been told its not the correct answer. Would someone like to help?
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### The smallest amount

Using a pool of problems, 20 tests will be formed. -Every test should have the same number of problems. -Any problem should be included in at most 10 tests. -For every 5 tests, there should be at ...
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### Birds Problem-Brain Teaser- Amazon interview question

Three people consider as A,B,C went for sight seeing. A,B and C each individually saw a bird that no other saw.(Eg: If A saw a bird the same is not seen by B and C) Each pair saw a yellow bird that ...
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### An interesting puzzle

Here is a puzzle challenge for you: Suppose $X,Y$ are independent and identically distributed Random Variables. Show that $$P\{|X-Y|\le2\}\le 3P\{|X-Y|\le 1\}$$
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### black and white balls in the box

A box contains $731$ black balls and $2000$ white balls. The following process is to be repeated as long as possible. (1) arbitrarily select two balls from the box. If they are of the same color, ...
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### Puzzle in Percentages

Okay, this is a real-time problem. The following is a picture of Customer satisfaction rating, which was displayed next to an item in an online shopping website. Satisfied customers click the ...
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### Applied Probability with Four Disjoint Subsets.

I have a rather longwinded question, so please bear with me! A number of employees conduct duties at company X. Each type of employee meets by department 4 times yearly. Occasionally, a ...
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### Probability Puzzle : Robot and coins

Someone walks into your room and dumps a huge bag of quarters all over the floor. They spread them out so no quarters are on top of any other quarters. a robot then comes into the room and is ...
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### Correct application of birthday problem

The problem is as follows: There are 10 shooters at a shooting range. Each shooter is given 5 bullets. They all begin shooting at 9am and end shooting at 10am, They each shoot all 5 of their bullets ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...