0
votes
3answers
49 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
2answers
19 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
512 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
46 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
21 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
34 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 ...
4
votes
2answers
64 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
63 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
23 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
41 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
58 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
88 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
56 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
45 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
37 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 ...
2
votes
0answers
46 views

hat matching problem (Ross, p.41)

I'm studying Ross's probability book, and kind of got stuck on the matching problem. Suppose that each of N men at a party throws his hat into the center of the room. The hats are first mixed up, and ...
0
votes
1answer
39 views

Expected Value Intermediate Counting Problem

A palindrome is chosen at random from the list of all 6-digit palindromes, with all entries equally likely to be chosen. (Recall that a palindrome is a number that reads the same forward and ...
2
votes
1answer
93 views

Tough combinatorics problem

We have an urn containing $n_a$ tiles labelled "A", $n_b$ ones labelled "B", and $n_c$ tiles labelled "C". We also have a string of letters consisting of $s_a$ occurrences of the letter "A", $s_b$ ...
0
votes
2answers
76 views

please help me ( probabilities )

please let me know if my answer true or false Three numbers are chosen at random without replacement from the set {0, 1, 2, 3, ... , 10}. Calculate the probabilities that for the three numbers drawn ...
1
vote
2answers
35 views

Counting exercises - Solution verification.

i'm studying some combinatorics and i came up in the following exercises. Suppose we are given a set $U$ of $n$ elements. Suppose $A \subset U$ has $k$ elements. Determine the number of subsets ...
1
vote
1answer
73 views

Expected value over many trials

I am a poker player and was talking to my friend about expected value. He claimed that if you play far enough above your bankroll, expected value can be negative, even if you have a skill edge. I ...
-1
votes
1answer
44 views

Probability of 1 at both end of string

Given a string S having N characters long and consists of only 1s and 0s. Now given an integer K, let us pick two indexes i and j at random between 1 and N, both inclusive. What's the probability ...
2
votes
1answer
58 views

Count 1-bit in binary integers

Given an integer range [A,B], (1) What’s the probability to get a 1-bit if we first randomly choose a number x in the range and then randomly choose a bit from x? (2) What’s the expected number of ...
2
votes
2answers
18 views

Probability distribution of selecting combinations of green and yellow balls from a set of green/yellow/red

Let's say I have G green balls, Y yellow balls and R red balls. I'm interested in ...
4
votes
4answers
404 views

Probablity that 3 husbands sit next to their wives round a circular table

There are 3 couples sitting randomly round a 6-seater circular table. What is the probability that all the husbands and wives sit next to each other? My attempt: First wife, say, takes any of the ...
2
votes
1answer
42 views

Combinatorial Probability

Another exercise from Saeed Ghahramani's Fundamentals of Probability, paraphrased below: Consider a train with $n$ cars and $m > n$ passengers. Suppose passengers board cars randomly. What is ...
2
votes
1answer
114 views

Why do probabilists have a preoccupation with urns? [closed]

Why is there an off-putting amount of questions from probability or combinatorics that involve an urn? Is there some historical reason? Did someone not have a box, or other container, on hand and had ...
4
votes
1answer
40 views

Derive a procedure to select one of the 2 options with equal probability when we are not using a fair coin.

Derive a procedure to select one of the 2 options with equal probability when we are not using a fair coin. $P(\text{H}) = p$. $P(\text{T}) = 1 - p = q$. I came up with the following two-roll ...
1
vote
0answers
82 views

Arranging numbers in a grid

I have a $n \times m$ matrix $M$ and a permutation of sequence $P$ of numbers from $1$ to $n$. I have to fill the matrix using numbers $1$ to $n \times m$ in such a way that for each row $i$, the ...
0
votes
3answers
38 views

Counting Number of even and distinct digits

The Question was: The number of even four-digit decimal numbers with no digit repeated. So the first digit cannot be 0 so there are 9 ways to choose a digit. Then for the 3rd, 2nd and 1st digits ...
0
votes
2answers
46 views

dice probabilities

please help me solve the following 2 questions. I know the answers, but there was no help on how to get them. if I paid a dollar per point (333 pays 9, 444 12, 666 18, 321 6), what's the maximum ...
0
votes
0answers
179 views

Distributing cards among players

Moderator Note: This is a current contest question on codechef.com. N players sit around a round table. There are $n \cdot m$ cards with unique numbers of range $1\ldots n\cdot m$. Each player ...
1
vote
2answers
70 views

Expected number of coin tosses needed until all coins show heads

We flip $n$ fair coins every iteration of the game. Every coin that shows heads is removed from the game and we use the remaining $n-k$ coins to play the game again (where $k$ is the number of heads ...
2
votes
0answers
52 views

Probability of getting not two head consecutively on tossing a coin ten times?

I am working on this problem and found total number of favourable cases 144 as $$1 + 10 + \binom{9}{2}+ \binom{8}{3}+ \binom{7}{4}+ \binom{6}{5}$$ and answer in the book is 128 favourable cases ...
1
vote
2answers
41 views

SAT Probability of 4…

X _ _ X The figure above represents four offices that will be assigned randomly to four employees, one employee per office. If Karen and Tina are two of the four employees, what is the probability ...
0
votes
1answer
33 views

Predict number of Birthdays for 1000 person of same class in next 365 Days

I want to know an approximate number of birthdays for a class where each month 1000 Persons are added up. Like 1st month its 1000, 2nd month its 2000, 3rd month it is 3000 And so on. Now lets say ...
0
votes
1answer
43 views

combinatorics & probability problem

There are numbered cards 1 to 13 each of colour red, green, yellow and white. And four players have been distributed 4 each of these cards randomly. What is the probability that each player gets ...
1
vote
1answer
36 views

Iterate through n coins flipping these obtaining all possible combinations.

If I have let say n coins all facing the same way. Is there an iterative method for turning these coins, one at a time, until all possible combinations have occurred one and only one time? This is ...
0
votes
1answer
35 views

Estimating number of customers

I'm trying to analyze a simple model for businesses. I'm not sure if the problem I'm having is with notation. There seems to be some discrete structure I don't understand how to write down or ...
2
votes
3answers
19 views

Solution check for counting in a list

This problem involves lists made from the letters T,H,E,O,R,Y, with repetition allowed. How many 4-letter lists are there that don’t begin with T, or don’t end in Y ? Just want to make sure my ...
0
votes
0answers
36 views

two correlated process

I apologize if this question is not placed in the right place. But I am having a hard time to figure it out. It would be greatly appreciated if some one could help me out. Assume that there are two ...
0
votes
0answers
52 views

Probability with dice sum K

Alice rolls a N faced die M times. she adds all the numbers she gets on all throws. What is the probability that she has a sum of K. A N faced die has all numbers from 1 to N written on it and each ...
1
vote
3answers
79 views

4 heads in 8 tosses

If someone asked me the odds of getting 4 heads in 8 flips of a fair coin. I would initially think to do something like this: $\dfrac{2^8 - \left( \binom{8}{0} + \binom{8}{1} + \binom{8}{2} + ...
2
votes
0answers
31 views

Probability that half the nodes has more than half out-degree

This is something I just wondered about, and I don't know whether there is a closed-form answer or not. I've tried but without making progress, so any idea would be helpful. Consider a complete graph ...
3
votes
1answer
59 views

What is the joint probability distribution of number of balls after $n$ draws?

The following problem came into my mind when I am studying the Polya Urn Model. At the beginning, from a bin containing $c_1$ balls labeled $1$, $c_2$ balls labeled $2$, … , $c_m$ balls labeled $m$, ...
0
votes
2answers
46 views

SAT Math probability and repeats

A ball's area is divided into two sections. If each section is to be painted using one of 5 different colors, how many differently painted designs are possible? I know that the first area has 5 ...
1
vote
1answer
53 views

52-card deck probability…

If 13 players are each dealt four cards from a 52-card deck, what is the probability that each player gets one card of each suit? So I chose to do the situation where we have no repetition (i.e ...
5
votes
1answer
69 views

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 ...