# Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

67,666 questions
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### what is the probability that in the second box we have 2 red balls? [closed]

We have two boxes. In the first box, there are one red and one white ball. In the second box, there are either one red and one white ball or two red balls. We take out one ball from each box at the ...
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### The probability that $3$ organizers win

A local fraternity is conducting a raffle where $55$ tickets are to be sold - one per customer. There are $3$ prizes to be awarded. If the $4$ organizers of the raffle each buy one ticket, what are ...
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### Identify which normal distribution generated a given sample

I have $d$ Normal Distributions, $N_1(\mu_1, \sigma_1^2) \cdots N_d(\mu_d, \sigma_d^2)$. We pick one of the $d$ distributions with each distribution having a probability of $\frac{1}{d}$ of being ...
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### Using Excel to Solve a Statistics and Probability Delivery Driver Problem [closed]

Frankie has heard his delivery drivers complain that they don’t have enough time to complete their scheduled deliveries, and he observed that it has been a while since he hired a new driver. The ...
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### Maximize expected utility of reward [closed]

This task is given from DeGroot Optimal Statistical decisions book.
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### Necklace is made out of ten different red, twenty different orange and thirty same yellow pearls.

Necklace is made out of $10$ different red, $20$ different orange and $30$ same yellow pearls. If we know that no two red pearls are next to each other, what is the probability of the case where ...
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### Probability regarding computer science

Consider the following program segment: if B then repeat S1 until B1 else ...
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### Hypergeometric Probability - Average chances after multiple trials

Hopefully someone can help me out here. I'm stuck on a few hypergeometric probability calculations I'm working on for an assignment. I'm stuck on finding the average chances from Trial 3 and onwards. ...
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### Discrete mathematics: chances of getting specific card on card-game

The game is played with a deck of $40$ cards. Three of them are dealt to each of two players, so my hand, the cards that were given to me, is formed by three cards of the deck. At the same time, ...
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### trying to figure out the pvalue if I know the significant level of 0.10 the critical values of -1.935 and 1.935 and degrees of freedom is 14 [closed]

trying to figure out the P-value if I know my significant level of 0.10 and critical values of -1.935 and 1.935 and degree of freedom is 14. My calculator is broke .
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### How many ways are there to arrange three groups of people around a circular table?

I have the following question: Three Koreans, three New Zealanders and three people from Bosnia are seated at random around a round table. What is the probability that the people in the three groups ...
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### A jar contains $2$ pennies, $6$ nickels and $4$ dimes. A child selects $2$ coins at random without replacement from the jar. [closed]

A jar contains $2$ pennies, $6$ nickels and $4$ dimes. A child selects $2$ coins at random without replacement from the jar. Let $X$ represent the amount in cents of the selected coins. a. Find the ...
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### A variant of the boy/girl paradox

Some friends and I were arguing about the two following word problems, which are variants of the classic boy/girl paradox. (i) "Mrs.Smith lives in a world where the eldest child is always male. She ...
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### Gambler´s ruin for a Binomial multiplicative process

I would like to calculate the gambler´s ruin probability in a generalization of the classic gambler´s ruin problem. In the classical model, the gambler´s wealth could be modeled by an additive random ...
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### Entropy of a race and information of a message [duplicate]

Having 17 people running a race, the 1st runner have 3/4 probability of winning and all the others have (each) 1/64. The entropy of the marathon is 1.811bits.Knowing that the 1st runner didn't won ...
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### Markov Chain involving gerrymandering in Pennsylvania.

I am currently working on a project that involves the use of analyzing the 18 districts of Pennsylvania and using the results of the 2018 house of reps congressional election. I understand that ...
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### Probability density of the product of independent identically distributed random variables

Let $X_1, X_2, \dots , X_n$ be a random sample from the PDF $$f(x;\theta)=\theta x^{\theta -1},\;\; 0<x<1,\;\; \theta > 0$$ What is the probabilty that $\prod_{i=1}^n X_i > t$? The joint ...
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### Minimise a function of 3 variables.

If I have a function of 3 positive variables, $k$, $m$ and $n$, how can I find what value of $k$ minimises this function (in terms of $m$ and $n$)? The particular function I'm interested in is this: ...
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### If $E[X|Y= y] = y^2$ for all $y$, does it follow that $E[X| Y] = Y^2$?

Let $X,Y: \Omega \to \mathbb{R}$ be two discrete random variables on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$, and $\mathbb{E}[|X|]< \infty$. Suppose that $\mathbb{E}[X|Y=y] = y^2$ ...
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### What is the distribution of a nested Laplace?

We have three random variables $X_1, X_2, X_3$ having the following conditional distributions: \begin{align} p(X_2 \mid X_1=x_1) &\sim \mathrm{Laplace}(X_2;x_1, b) = \frac{1}{2b} \exp(-\frac{|X_2 ...
I'm trying to find the expectation of a stopping time. Specifically, Let $T_1,...,T_n$ be i.i.d exponential random variables with mean $1$. Let $S_n = T_1 + ... + T_n$ denote their partial sum. ...