0
votes
3answers
51 views

Need help with flaws in statistical reasoning

The problem is as follows - there are three couples and six chairs in a row. The six individuals are seated at random. What is the chance that at least one couple will be seated together? Here's my ...
2
votes
2answers
98 views

Hat Matching Problem Expectation

I have an interesting problem in the context of the hat matching problem: There are n people with hats at a party. Each person randomly grabs a hat. A match occurs if a person gets his own hat. I'd ...
1
vote
2answers
20 views

Permutations and Sample Spaces

Suppose 3 cars can either turn left $(L)$, turn right $(R)$, or go straight $(S)$. I need to find the sample space for all the possibilities but I am not sure how to do that. I know that for 3 cars ...
1
vote
0answers
21 views

Probability to find Divisibility of an integer by prime numbers [closed]

What is the probability that a positive integer n<100 is divisible by a prime number p<100?
1
vote
4answers
72 views

How many integer solutions to$ x+y+z \le 6$ where $x,y,z$ are non-negative?

I understand the steps towards working this question out if $x + y + z = 6$, but what are the steps for an inequality?
0
votes
1answer
51 views

How many binary sequences of length 16 have exactly eight 1’s? [closed]

How do I go about working out the number of permutations of a 16 digit binary number with 8 "1's"? Thanks for your help.
0
votes
1answer
33 views

The probability of choosing a particular color combination of balls after five draws

Sorry if this has been asked before, i can't get my head around how to take into account that the order of the balls being drawn is not important.
4
votes
0answers
36 views

Permutation order statistics integral

Let $U_i$ be $[0,1]$ i.i.d. uniform random variables, for $i=1,\ldots,n$. As an example, let $n=3$. Now pick an ordering, say $x_1>x_2<x_3$. and consider the order statistics integral ...
1
vote
3answers
63 views

5-letter strings using the letters in the word “EVERGREEN”

From the word EVERGREEN, 5 letters are chosen at random and arranged into a string of letters. What is the probability that this string is palindromic?
0
votes
1answer
57 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 ...
0
votes
1answer
37 views

Number of ways to choose 6 cards with the same suit from a normal deck of cards

In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present? One way was $\binom{13}{1}\binom{13}{1}\binom{13}{1}\binom{13}{1}$ but it involves repetition of ...
0
votes
3answers
46 views

What should n be so that the probability is less than 0.5 [duplicate]

n represents the number of people. The probability is that none of these people have a birthday on the same day. Neglect people that are born on 29 February. What should n be so that the ...
2
votes
1answer
49 views

Where can I find a set of probability problems?

Is there a database of solved probability problems available? I am currently studying probability (and statistics) and, while I think I have a decent grasp of permutations, combinations, conditional ...
-1
votes
1answer
38 views

Odds to guess a 32 byte value [closed]

I have 1,000,000 records, and each is assigned a 32 byte (3.4E+38) random value. What is the likelihood to guess one of the random values? Context This comes up in information security context: ...
0
votes
0answers
54 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
2answers
56 views

Probability query

8 Indians and 3 Americans are to stand in a row at random. What is the probability that no 2 Americans are always together? I think the answer should be 1 because as there are many possible ...
0
votes
2answers
97 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 ...
0
votes
1answer
17 views

Relationship between the probability two items in a list are correctly relatively ordered and the probability of any item being in the right place

Given a disordered list a of size n, and an ordering on the items of a, is there a relationship between the probability that two items are correctly ordered ($P(a_i \leq a_j)$ given $0 < i < j ...
1
vote
0answers
87 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
0answers
49 views

What Will be permutation of this question?

Sereja call two arrays A and B with length n almost equal if for every $\,i (1 \le i \le n), CA(A[i]) = CB(B[i])$. $CX[x]$ equal to number of index $j (1 \le j \le n)$ such that $X[j] < x$. For ...
0
votes
1answer
34 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 ...
1
vote
0answers
35 views

For $k$ random perms of an $n$-set $\mathrm{Pr}[\sigma_1\cdots\sigma_k=\sigma_k\cdots\sigma_1]\xrightarrow{k\rightarrow\infty}\frac{2}{n!}$?

Q. Fix $n \geq 2$, and choose $k$ random permutations $\sigma_1\sigma_2\cdots\sigma_k \in S_n$ uniformly at random. Is true that ...
10
votes
2answers
171 views

Probability of $\alpha\beta\gamma=\gamma\beta\alpha$ for random permutations of a finite set?

Following up on my previous question Probability that two random permutations of an $n$-set commute?, here's a related question for three elements. Q: If $\alpha,\beta,\gamma$ are chosen uniformly ...
3
votes
1answer
49 views

Possible permutations of a 3x4 cube puzzle

My kids have this 3x4 cube puzzle, you know, the one where a picture is formed if you assemble the cubes correctly. In reality you can create 6 different pictures, using different sides of the cubes. ...
4
votes
2answers
74 views

Probability that two random permutations of an $n$-set commute?

From this MathOverflow question: It is well known that two randomly chosen permutations of $n$ symbols commute with probability $p_n/n!$ where $p_n$ is the number of partitions of $n$. -- Benjamin ...
0
votes
3answers
32 views

DNA Sequence Distinct Way

we know The genetic code is based on the four nucleotides adenine (A), cytosine (C), guanine (G), and thymine (T). These are connected in long strings to form DNA molecule. with three A, one C, two G ...
1
vote
0answers
35 views

How many different sequences in this event?

There are $10$ students in the class. Four of these students will be selected randomly to participate in the math contest. Then, how many different sequences can four students be selected? I thought ...
0
votes
1answer
31 views

probability of finding a small sequence within a larger sequence

I'm wondering how to define the probability of a long string LS (using 26 letters alphabet) to contain a smaller string ss. Right know I have something like this. Number of LS containing ss: 26^( ...
0
votes
2answers
60 views

Probability of boys ahead girls

There are three boys and two girls in a Queue. What is the Probability that number of boys ahead of every girl is at least one more than number of girls ahead of her. My Try: Let $B1$,$B2$,$B3$ are ...
2
votes
2answers
39 views

A Circular permutation problem

i've this problem that's making me crazy. I've 12 ball, 4 of these are red, the others are white. What's the probability to obtain a circular sequences of balls in which red balls are not adjacent? ...
3
votes
1answer
64 views

Mean and Variance of Correct Answers for various ways of Multiple Choice Questions

I picked this question out of the blue while thinking about multiple choice questions. Consider I set, say $8$ multiple choice questions. Now, I want to find out, out of the three methods below, what ...
0
votes
2answers
56 views

Probability: What is wrong with my approaches?

$4$ out of $20$ balls are black. The others are white. If I pick $2$ balls out of those $20$ randomly, what is the probability that at least one of them is white? I could do this using a ...
0
votes
1answer
23 views

Ordered Partitions

I'm having trouble figuring out exactly how one would get the answer for a question such as: "how many ways can 9 concert tickets be divided between 4 concertgoers, such that one person receives 3 ...
0
votes
3answers
95 views

Probability: deep understanding of permutations and combinations.

Look at this problem: If one is to throw $2$ dice, what is the probability that he/she gets a total of exactly $4$ dots? Well, the amount of the events that satisfy the condition is $3$ as we ...
1
vote
1answer
28 views

Finding number of possibilities of n number of r combinations of which x can be unique behavior

I have say 5 alphabets altogether (a, b, c, d, e) out of which 3 (a,b,c) are from Bag 'A' and 2 (d,e) are from Bag 'B' I want all possible combination of 3 alphabets of these 5. so I used ...
1
vote
2answers
27 views

Permutations and probability related

A permutation of $1, 2, ..., n$ is chosen at random. Then the probability that the numbers 1 and 2 appear as neighbours equals (A)$\frac{1}{n}$(B)$\frac{2}{n}$(C)$\frac{1}{n-1}$(D)$\frac{1}{n-2}$ Is ...
1
vote
1answer
39 views

Choosing a sample from a sample probability

I am a bit confused about this problem. I understand that you need to pick a sample first, K, and then find the probability of that sample being red, L. The total different combinations of picking a ...
0
votes
1answer
31 views

Counting cases?

I don't have a background on probabilities but i do want to get the rule to solve the following problem and similar ones . Let's say we have a 2x2 matrix , in which every element could be either 1 or ...
0
votes
0answers
36 views

Probabilities with combinations/permutations?

There are two bags of twelve marbles, labeled 1-12 in each bag. Person A and Person B are each given a bag. Person A is going to randomly select three marbles from their bag. How many marbles does ...
5
votes
2answers
82 views

probability of sequence of integers

Suppose you have numbers from 1 to 10. You can choose four of them but the contiguous numbers should have an absolute difference greater than 1. For example, you can choose $$ 1-3-6-10$$ $$ 4-2-5-1$$ ...
0
votes
1answer
21 views

permutations and combination

How many different strings of lights can be created by placing 40 coloured lights on a horizontal string if 12 of them are red, 6 are blue, 14 are green and 8 are yellow? Assume that lights of the same ...
0
votes
1answer
54 views

Bridge hand Combination/Permutation

A Bridge hand consists of 13 cards from a deck of 52 cards. In how many ways can a (bridge) hand consisting of 5 spades(♠), 4 hearts(♥), 4 diamonds(♦) and 0 clubs(♣) be selected?
1
vote
1answer
50 views

Envelopes and Mailboxes

We suppose $n$ and $p$ are two positive integers. A) In how many ways can you divide $p$ identical envelopes in $n$ mailboxes? (Each mailbox can hold several envelopes at the same time) B) In how ...
0
votes
1answer
37 views

Probability of item distribution with a restriction

I'm having a hard time analyzing my research data, and was wondering if anyone had any suggestions? I've reworded the question so it is presented more like a statistics problem. There are $x$ number ...
0
votes
1answer
27 views

Permutation and combination regarding two people together

You have 11 friends and can invite 5 to dinner 1) in how many ways if two of the friends married and will not attend separately? 2) in how many ways if two of them are not on speaking terms and will ...
0
votes
1answer
42 views

Permuation & combination on finding number of ways lid can be wrongly placed

There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the ...
0
votes
1answer
33 views

What number of robbers, under the model of the prisoner's dilemma, would be optimal?

The prisoner's dilemma is defined as "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with ...
1
vote
5answers
681 views

Probability [Sum of digits is even for a random number] [closed]

A number of 6 digit numbers is written down at random. Probability that the sum of the digits is an even number is? Please answer with explanation.
1
vote
2answers
179 views

Probability [Distinct balls in distinct boxes]

6 different balls are put in 3 different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is ? Could anyone pleases give the answer and explain it.
0
votes
1answer
211 views

How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4 (if repetitions are not allowed)?

My Approach: Total no of available digits: 5 No of 1-digit formed: 5 No of 2-digit formed: 4(excluding '0' on ten's place) * 4 (including zero - one among given digits already used) No of 3-digit ...