# Tagged Questions

7 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
107 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 ...
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### 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 ...
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### 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 ...
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### 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.
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### 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 ...
134 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 ...
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### 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 ...
136 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?
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### 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. ...
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### 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 ...
86 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 ...
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### 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 ...
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### 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 ...
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### Green balls and Red balls, probability problem

I'm studying for my exam and I came across the following draw without replacement problem : ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 = ...
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### 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 ...
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### 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 ...