1
vote
2answers
104 views

What is the probability of going bankrupt in roulette?

Imagine that the bank has the money $M_1$ and the player has the money $M_2$. The rules are the following: You win with a chance of $\frac{17}{36}$ and lose with $\frac{19}{36}$ each round. Now you ...
0
votes
0answers
39 views

Card Shuffling and Convergence in Probability

There are $4n$ cards, and we denote the set of cards with number $4k,k \in \{1,2,\ldots,n\}$ as $S$. The we shuffle the whole cards randomly, which means that each permutation will happen with the ...
16
votes
2answers
294 views

The expected outcome of a random game of chess?

Imagine a game of chess where both players generate a list of legal moves and pick one uniformly at random. Q: What is the expected outcome for white? 1 point for black checkmated, 0.5 for a ...
1
vote
2answers
53 views

Concept of Probability in math first level

I am trying to teach myself the concepts of probability and I was wondering if this is correct. I am only 13 years old and did not learn this yet. I am just reading parts of a probability book to get ...
-1
votes
1answer
58 views

Mean and Standard Deviation self thought problem

I am 13 years old trying to teach myself about standard deviation and was wondering how this problem would look like. I know I am young to be learning this but I was reading about this and got ...
5
votes
1answer
50 views

At what point discrepancy, in the NBA, does it make sense to milk the shot clock?

I am admittedly not great with probabilities, so I am soliciting the help of the community. I am watching game 3 of the NBA Finals and I am trying to work out when it makes sense to milk the shot ...
4
votes
2answers
104 views

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 ...
1
vote
2answers
84 views

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 ...
12
votes
4answers
612 views

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?
1
vote
2answers
28 views

Efficient random guessing

Let $(x,y)$ be a random point on the plane with some unknown continuous distribution. Your opponent randomly chooses one of the coordinates and tells you. You shall guess whether this coordinate is ...
0
votes
3answers
113 views

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, ...
4
votes
4answers
251 views

What does “twice as likely” mean?

Once in a while I hear people say something like X is twice as likely as Y. What they usually mean is: $$p(X) = 2 \cdot p(Y)$$ and - in the context they refer to - they usually have $p(Y) < ...
5
votes
0answers
132 views

Coding Theory Problem to save Humanity

For starters, this problem doesn't originate from me, it's a friend's coding theory problem and I got interested, thinking about it, but I can't think of any as I only have very basic coding theory ...
37
votes
1answer
891 views

How likely is it not to be anyone's best friend?

A teenage acquaintance of mine lamented: Every one of my friends is better friends with somebody else. Thanks to my knowledge of mathematics I could inform her that she's not alone and ...
1
vote
1answer
64 views

NCAA bracket and binomial coefficients

Given that March Madness is almost here I was trying to figure out the probability of constructing a perfect bracket if you just flipped a coin for every game. I came up with two possible solutions. ...
0
votes
0answers
27 views

Probability of getting it right, when choosing answer at random. [duplicate]

So there has been this question going around on social networking sites, If you chose an answer to this question at random, what would be the probability of your getting it right? a) 25% ...
4
votes
1answer
294 views

BINGO Probability: Controlling average game duration

I wandered over here from StackOverflow and my understanding of advanced mathematics is limited, so bear with me... A standard, BINGO game card has 24 numbers arranged in a 5x5 format. The center of ...
2
votes
0answers
67 views

How much advantage would a Blackjack player gain by being able to see the underside of cards?

In the novel Spaceland by Rudy Rucker, the protagonist Joe Cube is grafted with an eyestalk that sticks vout into the fourth dimension. This lets him see under and inside three-dimensional objects ...
3
votes
2answers
283 views

How to choose between an odd number of options with a fair coin

It is possible to choose between three equally desirable outcomes by tossing a fair coin as follows: Choose option 1 if the first head appears on an even toss Choose option 2 if the first tail ...
0
votes
0answers
43 views

Waiting Time For Computer Cluster

There are $n$ computers. Computer users stay on their computers for a certain amount of time, $t$, throughout the day. Computer users come and go. How long will I have to wait, min/max, for a computer ...
1
vote
1answer
75 views

Mismatching Results - Keno and Probability

In Keno, a player picks from 1 to 70 (at least in this version), 20 of these numbers are drawn, and the payouts are based on the number of matches. What I have tried to do is to check that the Swedish ...
0
votes
2answers
71 views

Sample paytable for slots

Could I get a sample paytable with at least $10$ combos for a $4$ reel slot machine with $6$ symbols on each reel with a house edge of $1 \%$? Pay table is the combinations in which you win for ...
1
vote
1answer
75 views

Probability puzzle - Two people drawing marbles… what is the probability one will be the first to get a certain color

One of my relatives had a probability question that they asked me that was a little puzzling... What do you think? Can anyone explain how to do a problem like this? A container has six yellow ...
6
votes
2answers
194 views

Average complexity of random-pick comparison sort

Motivation. Suppose we have a number of images that we want to arrange in a linear order from the prettiest to the ugliest. At our disposal we have a trained aesthete, whom we can show two pictures ...
1
vote
2answers
158 views

Is there any surprising elementary probability problem that result in surprising solution like the Monty Hall problem?

For recreational purpose, i haven't seen a interesting elemetary probability question quite a while. Is there any surprising elementary probability problem that result in surprising solution like the ...
0
votes
1answer
39 views

Probability, something easy!

Good afternoon people suppose the function $$f\left(x\right)=\frac{sx^{2}}{zx^{2}+1}$$ How many different functions can there be, if numbers s and z are taken randomly from the set $\left\{ ...
0
votes
0answers
32 views

What are the odds of reaching the end of a random choice path without repeat choices?

Given $m$ balls in a container, having $n\le m$ colors, if balls are chosen from the container randomly without replacement until all balls have been removed and the order of choices is considered, ...
2
votes
1answer
95 views

Very tricky probability

I just came by this "easy" question but i am abit worried, ill tell you why. ...
4
votes
0answers
110 views

Card game probability

Suppose the following solitaire with a standard deck. I turn four cards visible on the board and on each turn, I remove those suits that appears more than once in the board. Then I fill the board such ...
11
votes
1answer
271 views

What am I getting for Christmas? Secret Santa and Graph theory

I live with four people, who thankfully don't spend much time on maths.se. We decided this year that we'd do a Secret Santa. We can represent the arrangement of who's buying for whom using a directed ...
3
votes
2answers
311 views

Expected number of points on circle to form an acute angled triangle

This problem was asked to me in an interview. We keep on adding points on a circle uniformly until there exist three points on the circle which form an acute angled triangle. What is the expected ...
2
votes
1answer
76 views

Throw dice, what does this mathematical expression mean in real life?

Assuming we have a dice and the event that if we throw dice for the k-th time and get a 6 is given by $A_k$, is there an actual explanation what $A:= \cap_{i=1}^{\infty} \cup_{j=i}^{\infty} A_j$ is?
3
votes
3answers
145 views

Trying to work out the probabilities of a dice game I used to play

At college, my friends and I would sometimes waste time playing a game with dice. We would roll 25 dice, pick out all the dice that landed on a 6, then roll the rest. This would carry on until all the ...
1
vote
1answer
52 views

Guessing Game Stochastic Optimization

This is part of another post I did, but I think it has interest in its own right: Let $Y =\{X_{1},X_{2}...X_{N}\}$ be a set of $N$ random quantities with assocated set of distributions ...
5
votes
1answer
152 views

Surprising limit (probability of no two coinciding pairs)

I stumbled upon this question by random chance. The motivation is kind of long, the question is pretty short; if you're just here for the limits, feel free to skip to the break. I'm taking five ...
2
votes
3answers
132 views

The game of hand cricket.

(If you could add a more suitable title, I'd be very grateful to you) My friend gave me this question: In the game of hand-cricket (hand baseball, if you like it :D) two players $X$ - the batsman ...
0
votes
2answers
78 views

Selection minimum out of $n$ different objects!

Suppose we have $n$ differnt persons and $n$ different objects.They have to select from the the objects such that every pair of person has at least one uncommon object. What is the minimum number of ...
0
votes
3answers
225 views

Ways to select donuts

Wanted to share this puzzle: A restaurant offers choice of six different types of donuts, each available in unlimited quantity. How many ways can you select three donuts? You can pick any number of ...
1
vote
0answers
75 views

Probability of occurrence of games in a football league

This question just came to me as I was watching a football game. There is a football league with 20 teams. Each team has to play every other team at home and away, which means each team will play a ...
2
votes
2answers
190 views

Probabilities associated with negatively marked questions

First of all: not a native english speaker, and not a mathematician. Please explain as you would to your 10 years old son. I have 120 questions to answer True or False For each right answer, i ...
9
votes
3answers
712 views

What is the Probability that a Knight stays on chessboard after N hops?

Say a $8 \times 8$ chessboard as per picture. A position is represented here by co-ordinates $(x,y)$. A move is aslo considered as valid, where the Knight lands outside the chessboard [ For eg. ...
0
votes
0answers
124 views

Annoying the entire world

Okay, so I had this conversation with a friend: [7時41分48秒] Me: INTERESTING CALCULATION TIME (y)` [7時41分55秒] Me: if everybody who is annoyed [7時42分01秒] Friend: lol [7時42分01秒] Me: ...
3
votes
1answer
84 views

$k$ cards summing to $n$

This was a problem posted about probability involving Fibonacci numbers that I thought was really interesting so I decided to repost a portion of it regarding a general closed formula. The problem ...
22
votes
3answers
1k views

A gambler with the devil's luck?

A gambler with $1$ dollar intends to make repeated bets of $1$ dollar until he wins $20$ dollars or is ruined. Probabilities of win/loss are $p$ and $(1-p)$, and each bet brings a gain/loss of $1$ ...
30
votes
1answer
2k views

Minesweeper - Chance of one-click win

I'd like to know if it's possible to calculate the odds of winning a game of Minesweeper (on easy difficulty) in a single click. This page documents a bug that occurs if you do so, and they calculate ...
2
votes
2answers
85 views

Expected number of pieces of a chessboard

If n squares are randomly removed from a $p \ \cdot \ q$ chessboard, what will be the expected number of pieces the chessboard is divided into? Can anybody please provide how can I approach the ...
6
votes
1answer
820 views

Deriving the 37-percent rule for dating

I am trying to prove the theoretical "37-percent rule" for dating. The setup, if I remember correctly, is this. Suppose that you will meet exactly $N$ potential mates in your life, and you will meet ...
3
votes
1answer
168 views

65-card deck consisting of 13 ranks and 5 suits

** I FIGURED OUT 15 out of 16 cases. I don't understand the last case of RUNT. Anyone helps? I recently went to a math event and one person presented a weird card deck, consisting of 13 ranks and 5 ...
1
vote
0answers
30 views

Truchet tiles on a cube [duplicate]

We randomly place copies of the tiles into faces of the flattened cube. 1.Find the probability that the circular arcs on the Truchet tiles will form one loop, two loops, three loops and four loops? ...
0
votes
1answer
210 views

Finding probability that a person gets $7$ when rolling a pair of dice

*I STILL DON'T GET THE ANSWERS PROVIDED. PLEASE HELP! In a game, the participant rolls a pair of dice. If the result is a $7$, he wins. If the outcome is a number $n$ different from $7$, he continues ...