0
votes
0answers
23 views

Suppose that we have 4 white and 7 black balls - Probability Question [on hold]

Suppose that we have 4 white and 7 black balls in a bowl, and randomly select three of the balls. We are interested in knowing the probability that one of the balls is black and the other two white. ...
1
vote
1answer
22 views

Number of outcomes times probability of failure is number of failures?

I was hoping someone could spread some insight on why this is true? Suppose that in some situation, there are n! number of possible outcomes. Also, suppose that p is the probability of failure of ...
3
votes
2answers
50 views

Expected number of output letters to get desired word

I am using a letter set of four letters, say {A,B,C,D}, which is used to output a random string of letters. I want to calculate the expected output length until the word ABCD is obtained; that is, the ...
1
vote
1answer
32 views

Independent, Probabilistic, Event occurs once in a set of 10, Has 10 orientations. Probability?

I have ordered sets. Each index in the set is random and independent. Here is a sample of possible sets: X1 < X2 < X3 < X4 < X5 < X6 < X7 < X8 < X9 < X10: ...
0
votes
1answer
26 views

What are the odds that every team that lost the prior week would be facing a team that won the prior week?

I apologize in advance for a potentially elementary question but I cannot figure out how to even begin with this. We have 10 teams Half lost the first week, the other half won Second week, we all ...
0
votes
2answers
134 views

Conditional probability: At least 3 kings given there are at least 2 kings in the hand of 13.

My first "conditional probability" problem. Sorry for all the questions. My instructor doesn't make sense to the class. A hand of 13 cards is to be dealt at random and without any replacement from an ...
0
votes
2answers
30 views

probability, 2 chips drawn have either same number or color

I've viewed similar problems to this, but I'm not understanding the logic to the question and answers behind them. There are 5 red chips (each numbered 1, 2, 3, 4, & 5), and 3 blue chips (each ...
1
vote
3answers
41 views

Probability You Choose at least one chip of every color

There are 16 chips: 6 red, 7 white, and 3 blue. 4 chips are selected randomly and are not replaced once selected. What is the probability that at least one chip of every color is selected? I'm not ...
0
votes
0answers
20 views

What does a presentation on block design and Latin squares consist of?

I read the wikipedia pages of both and I just cannot understand these two concepts. I have a presentation on both of these topics next week and I need some headway on both of these topics.
3
votes
3answers
124 views

How many ways can $10$ digits be written down so that no even digit is in its original position

If I have the numbers $0,1,2,3,4,5,6,7,8,9$ written down in that order, how many ways can the $10$ digits be written down so that no even digit is in its original position? It would seem that I can ...
1
vote
1answer
156 views

How to convert a problem to a stars and bars problem?

Continued question from here. With certain questions I have $x_i$ being constrained by various different inequalities, I want to know how to remove these from the problem, to bring me back to a ...
-3
votes
4answers
72 views

Probability: Linear Seating Arrangement [closed]

Okay, I'm new at probability and statistics, so please try to answer this as thoroughly as possible and explain why you did everything, from using a specific number to why using factorials and ...
0
votes
3answers
189 views

How to use stars and bars(combinatorics)

How to use the stars and bars method? Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$ Where $x_i\in\mathbb{N}$ Is this the correct time to apply the method?
0
votes
1answer
32 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
38 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
2answers
87 views

Binomial theorem combinatorics derivation

We can split any term $(x+y)^n$ into a choice tree with $2^n$ path choices. Also, we can represent each factor in terms of $x^ky^{n-k}$ It is logical to deduce we can express this with summation ...
0
votes
0answers
166 views

Average deviation of group sizes

I consider $n$ elements randomly dispatched in $n_{G}$ sets. Denoting $s_{j}$ the number of points in set $j$, I then compute the average deviation $d$ as: $$ ...
0
votes
0answers
33 views

In how many ways can you make change for a dollar? [duplicate]

I know there are questions related to this on the site but they are not in the context I am looking for (basic statistics). This problem is at the end of the section introducing combinations and ...
1
vote
1answer
81 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
vote
3answers
35 views

Problematic Permutation Problem

i see a problem without any definition. would you please help me? i want to calculate the number of permutations of 1,2,...,1392 that 696 numbers be in the natural positions (from all numbers, 696 ...
0
votes
0answers
38 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 ...
3
votes
1answer
66 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 $m$, ...
4
votes
2answers
102 views

Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.

I have a problem from a homework which I've been struggling with. I normally wouldn't post homework here, but I've spent several hours trying to understand the correct way to solve this , to no avail. ...
5
votes
1answer
72 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 ...
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 ...
0
votes
1answer
133 views

A point in a circle is selected at random. Calculate probability that point is closer to centre than circumference

State any assumption(s) you make Well, I decided to draw a circle with a center at the origin of a Cartesian plane. It had radius r so it's coordinates on the axes were (0, r), etc. I then drew ...
0
votes
1answer
18 views

On a real line R points a,b are randomly selected such that -2<=a<=2 and 0<=b<=3. Find the probability that | a - b | > 1

Let's say that C is the set where |a-b|>1 So I suppose you could say plot it as coordinates where the x-axis (labelled a) is from [-2,2] and the y-axis (labelled b) is from [0,3]. Now |a-b| must be ...
2
votes
3answers
141 views

In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288

In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288 Please explain how to get this. I understand that we have GGGG => 4 ...
0
votes
0answers
14 views

Question about the poly-Euler preprint

I'm looking over the preprint on poly-Euler numbers, and I think there might be a typographical error on the third line because $j=0$ leads to a discontinuity. Could somebody explain the substation ...
0
votes
3answers
57 views

Count all events for k distinguishable items in n distinguishable bins

I want to count all the possible cases that I can distribute k distinguishable items in n distinguishable bins, for example for 3 items and 2 bins I have the next n^k the possible cases are: I ...
1
vote
1answer
34 views

Set Questions? Need someone to help show

I tried doing these and I have the answers, but I can only do A. Can someone show me how to do the rest? I have the answers but don't know how to get to them..
0
votes
1answer
52 views

A committee requires one accountant, two marketing agents..

A committee requires one accountant, two marketing agents, and four board members. If there are four accountants, three marketing agents, and seven board members available for selection in the ...
0
votes
0answers
25 views

How to measure how many % is done

Let's say that 100 people are going to two exams. They must pass both. In the first exam, 20% of people go forward to the next exam. In the 2nd exam, 50% of people complete and therefore complete the ...
0
votes
0answers
61 views

Possible combination of k unique pairs between two sets

Given two sets $S_1$ and $S_2$, where $|S_1| = n$ and $|S_2| = m$, I want to find all combinations of sampling $k$ unique pairs from the two sets without replacement. How many combinations are there? ...
2
votes
0answers
31 views

Number of elements and number of different basis of $\mathbb F_5^3$

Let $\mathbb F:=\mathbb F_5$ the field with five elements. (i) How many elements has $\mathbb F^3$? (ii) How many different basis has $\mathbb F^3$? My idea: (i) $\mathbb F^3$ has $5^3$ elements. ...
1
vote
3answers
61 views

Proof that the combination formula actually gives you the number of combinations

Ok, there's no problem in defining a binomial coefficient the way it this: $$\binom {a} {b} = \frac{a!}{b!(a-b)!}$$ I can also prove to myself that if I have $n$ elements, like: $\{a_1, a_2, \ldots, ...
-1
votes
3answers
54 views

Show that $C(n,k) = C(n-1,k) + C(n-1,k-1)$ [duplicate]

I'm studying for my final for Statistics, and I want to understand literally every problem in my textbook (at least in the first 7 chapters). One of the problems asks to show that ${n}\choose {k}$ ...
1
vote
1answer
33 views

What's the expected score for guessing on a word bank/“matching” test?

Some quizzes/tests have a "matching" or "word bank" section, which is set up as follows: There are $n$ questions that the student must answer. The answer to each of the $n$ questions is one of $k ...
0
votes
2answers
54 views

Combinatorics question - seats

In how many options can we arrange random number of men (identical men) in line of 15 chairs but: 1. 2 men can't sit next to each other. 2. next to each empty chair - there is at least one men. i ...
1
vote
2answers
72 views

Probability, chose two skittles, out of 2 skittles left from a bag of skittles with 5 colors.

so me and my friend are studying statistics but we are just stuck on this stupid skittle question we made up ourselves when we tried to guess the colors of the two last skittles so we can see who will ...
4
votes
2answers
168 views

Green balls and Red balls, probability problem

I'm studying for my exam and I came across the following draw without replacement problem : ...
1
vote
1answer
52 views

Probability: 30 balls in a bucket, homework

i need some help with some homework, first time i am doing probability and statistics, id like to know if my 2 answers below are correct, and how i can solve the remaining 2. There are 30 balls in a ...
5
votes
6answers
3k views

Fewest number of moves to win the game 2048?

I'm trying to figure out the fewest number of moves one could make to win the game 2048. In another thread, someone placed the figure at 520, but I'm wondering if anyone knows how to mathematically ...
6
votes
3answers
508 views

Why does the keyword “distinct” change the solution to much?

I don't understand why the second answer is different from the first. Aren't they the exact same thing? How many ways can we distribute 10 distinct balls into 5 distinct boxes? $5^{10}$ is correct ...
3
votes
2answers
387 views

What is the probability that $x_1+x_2+…+x_n \le n$?

Given that $X_1, X_2...$ are mutually independent random variables. For each $i$ with $1\le i \le n$ the variable $X_i$ is equal to either $0$ or $n+1$ $E(X_i)$ = $1$ also.. if $X_i$ is equal to ...
2
votes
1answer
84 views

Differentiate $P_{x_n}(z) = \prod_{i=1}^n\frac{1+z+z^2+…+z^{i-1}}{i}$ twice to calculate the variance of involutions.

Use the Probability Generating Function for Involutions: $P_{x_n}(z) = \prod_{i=1}^n\frac{1+z+z^2+...+z^{i-1}}{i}$ To Calculate the Variance of Involutions where: $Variance \space X_n = ...
1
vote
1answer
60 views

Largest Number Drawn - Why are These Approaches Not Equivalent?

Here's the question: Four numbers are drawn at random from a box of ten numbers 0, 1, ..., 9. Find the probability that the largest number drawn is a six if the draws are made with replacement. The ...
0
votes
1answer
42 views

probability equiprobable space?

For the problem below are we going to use the equiprobable space. Which is In particular, if S contains n points then the probability of each point is 1/n . For an event A, P(A) = number of elements ...
0
votes
0answers
27 views

2nd Question in introductory probability

There are the same number of red and blue people at a party. And decided to meet up the next day. 1/5 of the red people and 1/3 of all the people were missing. Calculate the probability that a ...
0
votes
1answer
31 views

Beginner question in probability

i'm a beginner in statistics and probability and i need help with a given problem please. We are given a guy who has a machine and a button, the outcames when he presses the button are: a)Music ...