2
votes
2answers
37 views

Probability problem: n different balls in n different boxes

Problem Suppose $n$ different balls are distributed in $n$ different boxes. Calculate the probability that each box is not empty when distributed the balls. I'll define the sample space as ...
0
votes
1answer
54 views

distribution of books among students

There are $p$ students and $q$ books where $q>p$ and all books are different, but each student will get a minimum of $1$ book and a maximum of $(p – 1)$ books. Find the total number of ways of ...
2
votes
2answers
37 views

Subset Probability to Element Probability

Is there any way to match (or map) from Subset Propabilities to Element Probabilities? Suppose that John may select x-sized subsets from a population of N items. In every subset he has exactly x ...
7
votes
1answer
123 views

The Day Camp Stacking Game

My friend works at a day camp as a counselor and he told me about an interesting game he plays with his group of kids. You have a perfectly shuffled, regular $52$-card deck and a group of $2 \leq n ...
0
votes
1answer
65 views

Help me (probability) [on hold]

Frederick and Paulo were conducting an experiment to see how many heads they could toss in 100 tosses of a coin. After 10 tosses they had 4 heads and 6 tails. Their friend Juliana came into the room ...
3
votes
0answers
72 views

What's so special about binomial coefficients that someone decided to organize them in a triangle?

I know that binomial coefficients are related to figurate numbers (which were studied by Greeks a loooong time ago, because of its connections to geometry). I also understand how the Pascal's triangle ...
1
vote
1answer
34 views

What is the probability that each of the vehicles will be made to carry at least one local tourist?

Three vehicles (one blue, one green and one grey) with a carrying capacity of 8 passengers each are to be used to ferry 18 international tourists and 5 local tourists (who are a family) from OR Tambo ...
1
vote
1answer
23 views

What is the probability that the maximum number of shots fired successively from a type A gun is $2$?

A gun salute always takes place at the funeral of a military leader who has died in a certain country. (The $21$ gun salute where $21$ rounds are fired - is the most common for the most senior ...
0
votes
2answers
30 views

Probability that the first $2$ balls are white, given that the sample contains exactly $6$ white balls

An urn contains $30$ white and $15$ black balls. If $10$ balls are drawn without replacement, find the probability that the first $2$ balls are white, given that the sample contains exactly $6$ ...
0
votes
2answers
47 views

6 Professors and 8 floors - expected value

I have this problem I need help with. There are 6 professors on an elevator that has 8 floors/stops. Each professors exits the elevator randomly(1/8 chance). What is the expected value E(X) of stops ...
1
vote
4answers
73 views

Probability of drawing at least 1 red, 1 blue, 1 green, 1 white, 1 black, and 1 grey when drawing 8 balls from a pool of 30?

Given a pool of 30 balls (5 of each color). When drawing 8 balls without replacement, what is the probability of getting at least one of each color? Related: Probability of drawing at least one red ...
1
vote
2answers
87 views

Probability of assigning balls into buckets, where each bucket has a certain capacity.

I'll start with a specific example of what I am trying to solve: I have eight balls to be randomly placed into four buckets. Buckets #1-3 have the capacity of 2, 2, 3 respectively, while bucket #4 ...
7
votes
0answers
108 views

How to estimate $Pr[vr_i=ur_i]$ in the presence of rotations

Suppose we want to compute the probability that for two different random vectors (with elements that are $0$ or $1$), denoted by $v$ and $u$, multiplying them with the rotations of a random vector $r$ ...
-1
votes
1answer
29 views

In how many of the possible arrangements will both end balls be of the same colour? [closed]

6 blue balls, 4 red balls, and 2 white balls are placed in a straight line. In how many of the possible arrangements will both end balls be of the same colour?
0
votes
1answer
31 views

Probability for incomplete information

Let's say there are 10 teams: A-J. Only 1 team wins, others lose. Probability of any team to win is unknown (different for each team) and to be calculated. Not all teams participate in each game. ...
0
votes
1answer
33 views

How to calculate probability that a team will win

Let's say there are 10 teams: A-J. Each team always participate in each of the game. Only 1 team wins, others lose. Probability of any team to win is unknown (different for each team) and to be ...
1
vote
1answer
34 views

Rolling 6 dice and 3 on the same side

I found similar answer for 'Rolling 6 dice and 4 on the same side'. Will exactly the same rule apply for 3 dice? Instead of 15000 (according to the above link), I found somewhere 14700. $${6 ...
0
votes
3answers
21 views

What is the probability that the newest of the first edition is next to the oldest of the second edition?

There are six copies of a certain textbook in a school library. They were all purchased at different times. 3 are of the first edition and the other 3 are second edition. They have been returned ...
0
votes
0answers
20 views

Bounding a specific function of binomial coefficients

While trying to directly prove the existence of expander graphs (e.g. http://www.cs.toronto.edu/~avner/teaching/S6-2414/TUT2.pdf), one uses the following inequality: $$\sum_{s=1}^{n/2} ...
-2
votes
2answers
58 views

What is the probability that no members of a married couple sit next to each other [closed]

Five people (A, B, C, D and E) dine at a round table. They take their places at random. A is married to B. C is married to D. E is single. What is the probability that no members of a married ...
0
votes
1answer
37 views

Round table seating - expected value

There are $p$ women, $s$ men and $p+s$ seats in a round table. Let $X$ be the number of women who sit between two men. Find the expected value of $X$. I know that expected value of $X$ is given by ...
3
votes
3answers
267 views

2 of 3 dice are selected randomly and thrown. What is the probability that one of the dice shows 6

1 red die with faces labelled 1, 2, 3, 4, 5, 6. 2 green dice labelled 0, 0, 1, 1, 2, 2. Answer: 1/9 Please can you show me how to get the answer. I'm confused about joining the events of choosing 2 ...
0
votes
1answer
53 views

2011 AIME Problem 12 — Probability: 9 delegates around a round table

Nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one ...
0
votes
1answer
23 views

Bernouilli trial with variable number of experiments

I'm kinda stuck on a probability problem I encountered in designing a game. Here is its description : I'm calculating the number of turns (Tf) before a integer variable (A) reaches 0. Each turn, A ...
0
votes
1answer
22 views

What is the probability of getting at-least one even digit for 5 trials.

Let we have through a fair dice. What is the probability of getting at-least one even digit for 5 trials. In this case I have evaluated the number of trials as follows: The probability ...
2
votes
2answers
52 views

A coin is tossed six times. What is the probability of getting at least four heads on the tosses?

A coin is tossed six times. What is the probability of getting at least four heads on the tosses? I have solved the problem like this: probability of getting 2 tail = ${}_6C_4 \times ...
0
votes
0answers
13 views

Slots Machine Matching feature 2

I'm designing a slot machine. I need to find the number of combinations that two matching icons will appear side-by-side in a 3X5 window (3 rows, 5 reels (columns)) A match gives the user some ...
1
vote
1answer
51 views

How to compute the expected number of unwatched rooms?

Imagine that I have a number of rooms, r, that I want to have watched. So I install one video camera in each room and have televisions that can show what's going ...
3
votes
5answers
1k views

Probability of guessing a PIN-code

A friend and I recently talked about this problem: Say my friend feels a little adventurous and tells me that exactly three of four digits of his PIN-code are the same, what is the probability that I ...
1
vote
0answers
40 views

A variation of the menage problem

A combinatorics problem I am chewing on without success is: 3 couples and 40 others are to be arranged randomly in a row. What is the probability that no two couples sit together ? I have looked at ...
1
vote
1answer
35 views

A question involving the throw of seven dice, which of my answers is correct?

Seven dice are thrown, what is the probability that all numbers show up on the dice? My first answer uses the logic that if all numbers show up and you throw seven dice, then one number is repeated ...
2
votes
2answers
40 views

Selecting 180 days from 366: the probability of even distribution across months, or not having September among the first 30

In a draft lottery containing the 366 days of the year (including February 29). Select 180 days (draw 180 without replacement). a) What is the probability that the 180 days drawn are evenly ...
5
votes
4answers
134 views

Probability that a word contains at least 3 same consecutive letters?

Assume we have a word of length $n$ and an alphabet of length $26$ (the small letters a through z, if you want so. How likely is it that this word contains at least $k := 3$ consecutive letters of ...
0
votes
3answers
82 views

Birthday paradox, huge numbers

Pick x random "birthdays", say $10^9$. What are the chance of a collision, given $2^{160}$ possible "days"? I'm trying to estimate the collision rate of sha1 hashes, but the calculation is too big ...
3
votes
3answers
44 views

Probability of having 4 aces after taking turns to pick cards

I've started to learn probability and I get stuck with the following problem: My friend and I are playing a card game with 36 unique cards. There are four suits (diamonds, heart, clubs and spades), ...
4
votes
2answers
544 views

Outcome of rolling a fair die 6 times

I'm failing to understand how to come to the answer to this question. If you roll a fair die six times, what is the probability that the numbers recorded are $1$, $2$, $3$, $4$, $5$, and $6$ in any ...
0
votes
0answers
53 views

The probability of random permutation leaving the sequence almost unchanged

So let's say I have $52$ completely different kinds of arenas that get shuffled. What are the chances of getting the exact same sequence if only one arena can be out of order? For example, you could ...
0
votes
1answer
23 views

Probability $\sum_{j=n+1}^{2n+1} {M \choose m+1}{M-m-1 \choose j-m-1}/{N \choose j} $

I have a prob. problem: A school has $N$ students in which $M$ students are leader (of each class in school), and $N>M$. There are $2n+1$ balls in the black box including $n+1$ blue balls and $n$ ...
1
vote
2answers
47 views

what is the > probability that only one letter will be put into the envelope with > its correct address?

Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at ...
5
votes
1answer
102 views

Probability of drawing a run of a specific color from an urn with two colors of balls

I was sent a puzzle involving an urn with 128 white balls and 288 black. If the balls are drawn without replacement until the urn is exhausted, what is the probability that a sequence of 10 or more ...
1
vote
1answer
41 views

Is there a set of 69 length-6-sets out of 46 numbers [1..46] so that those length-6-sets “cover” all possible 1035 length-2-sets of 46 numbers?

1.) For this question, we have 46 numbers (balls, cards, whatever): {1,2,3,4 .... 45,46} ======================= 2.) Each length-6-set of 46 numbers ( e.g. {1,2,3,4,5,6} or {1,13,16,17,32,46 } ...
0
votes
1answer
65 views

Combination Problem with Sofa [closed]

Suppose we have 5 sofa on room A. in this room, 4 students seated on these sofa. These Strudents go to another room for eating dinner, and after that come back to room A. how many way the students can ...
1
vote
1answer
63 views

Will I will be able to sit and watch the movie?

Recently I went to the theater. When I came to buy my $3$ tickets (two friends and I), the machine tells me that there is $18$ seats out of $300$ ($15$ rows of $20$ seats). What is the probability ...
2
votes
1answer
24 views

What are the probability that the first two rows of the class are full?

I was boring in my class. So I ask myself the question: What are the probability that the first two rows of the class are full? Knowing that we're $25$ students in my class and the class have ...
1
vote
0answers
44 views

The probability that exactly / at-least $k$ numbers are in the correct position [duplicate]

Given a sequence of $[1,\dots,n]$ in random order: Let $P_k$ be the probability that exactly $k$ numbers are in the correct position Let $Q_k$ be the probability that at least $k$ numbers are in the ...
4
votes
1answer
62 views

Simple counting problem

Suppose that you have a box with $n$ balls, from the $n$ balls $k$ are white and $n-k$ are black. Now, sequentially you draw (without replacement) the $n$ balls in groups of $m$ (a natural number that ...
0
votes
3answers
135 views

Math Problem on Probability

In the SmallState Lottery, three white balls are drawn (at random) from twenty balls numbered 1 through 20, and a blue SuperBall is drawn (at random) from ten balls numbered 21 through 30. When you ...
1
vote
1answer
59 views

Calculate single “battle” outcome odds for RISK

I am trying to reproduce the values in this odds ratio table from Wikipedia. For all those unfamiliar with RISK, this is a game where units fight against each other via the roll of the dice: The ...
2
votes
2answers
48 views

Estimate the number of ants in a colony

A friend of mine gave me this weird problem I cannot solve. To estimate the number of ants in a colony an entomologist draws 5500 ants randomly from the colony, labels them with a radioactive isotope ...
-2
votes
1answer
52 views

Expected Value Question Intermediate [closed]

Mila has four ropes. She chooses two of the eight loose ends at random (possibly from the same rope) and ties them together, leaving six loose ends. She again chooses two of these six ends at random ...