# Tagged Questions

This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under (...

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### Find the Probability of 2 Numbers A and B from Interval

Two numbers A and B are selected from the interval [−3, 2] with uniform distribution. (A) What is the joint probability density function for A and B? This is ...
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### Probability of event given PMF

Given a pmf $$p(k) = (1 - \beta)\beta^k$$ for $k=1,2,3,\dots$, $\mathbb{P}\left(\text{outcome is even number}\right) = ?$ The event space (the power set of positive integers) is countably infinite.
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### How to prove a statistic is sufficient using conditional probability argument?

I'm trying to tackle a question, but don't know how to start it: Components of a certain type are shipped in batches of size k. Suppose that whether or not any particular component is satisfactory ...
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### Tricky Probability Question not sure where to start

A bag contains x (inedible) regular rabbits and one chocolate rabbit. Two players in turn draw a rabbit at random without replacement from the bag, until the chocolate rabbit is drawn. The player ...
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### Buy more lottery tickets or more multipliers?

In a given lottery, let's say my odds of winning a grand prize are $p_0$, and the grand prize has value $V$. I can either buy more tickets, at a cost $C_1$, or for each ticket, I can buy a multiplier ...
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### In a raffle with 100 tickets, 10 people buy 10 tickets each. There are 3 winning tickets which are drawn at random.

What is the probability that there are three different winners? My thinking is that this is a hypergeometric set up but I do not know how to set it up. If $A$, $B$, and $C$ represent the event that ...
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### Correlation of uniform variables

Let $X$ and $Y$ be independent random variables, $X,Y \sim unif(0,1)$. Let $U = \min \{X,Y\}$ and $V = \max\{X,Y\}$. Find the correlation coefficient of $U$ and $V$. I think we can assume that $U = X$...
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### Picking codewords that are close

Let $[n,k,d]$ be a linear code over $\Bbb F_q$ with minimum distance $d$ and number of minimum weight codewords $N_d$. How many ways can you select codewords $c_1,\dots,c_T$ (assume $T\ll q^k$) such ...
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### If $P(Y^{2} \geq k) = 0.95$ is it true that $P(\sqrt{k} \leq Y \leq 1) =0.95$

Suppose $Y$ is a random variable defined on $[0,1]$, and that we know $Y^{2} \sim \mathrm{unif}[0,1]$. Suppose I determine the value of $k$ for which $P(Y^{2} \geq k) = 0.95$. Would it be correct ...
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### Weak * topology on a finite-dimensional simplex

I'm trying to endow a set of probability measures $\triangle\left(X\right)$ with the weak * topology, where $X=\left\{ x_{1},\, x_{2},\,...,\, x_{N}\right\} \subseteq\mathbb{R}$ is a finite set of ...
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### Probability of randomly selected balls being different colors

An urn contains 5 red and 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that they are all of the different colors if the balls are drawn without ...
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### Sampling from a population

I have a very basic propability question: There are 200 socks in my basket. 25 are white, the rest are black. If I pick 10 socks, what's the probability of picking 3 white ones? I tried to calculate ...
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### Expected number of transition events to complete multiple synchronized Markov chains

Assume the expected number of transitions (events) it takes until a Markov chain with $G+1$ states ranging from $s=0$ to $s=G$ is completed is $M$. Suppose we have $K$ independent instances of this ...
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### Find the expectancy of $X$

Let $p,q \in (0,1)$. Let $Y$ be the R.V denotes the number of days of the storm in the ocean. $Y\sim \text{Bin}(n,p)$. Let $X$ be the number of ships drowned during the storm and we know that the ...
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### A Bayesian problem of coin tossing

A box contains $3$ coins . Among these three , each of two coins have the probability of giving head $\dfrac 23$ and the remaining one have the probability of turning head $\dfrac 12$ . One coin is ...
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### subtracting mean of iid RVs increases mutual information?

I have a problem about intuition: substracting the mean of iid RVs seems to increase the mutual information. Say $X,Y$ are real iid RVs, then $\frac{X-Y}{2}$ and $\frac{Y-X}{2}$ are not independent ...
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### probabilityproblem

A and B play a game of chess. They play 20 games of which A wins 12 and B wins 4.The remaining 4 games are drawn.If 3 games are played between them, find the probability that i)B wins at least 1 game?...
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### What is the expected number of trials until at least $m$ successes without repetitions?

I tried to look for a similar question but didn't find the exact thing (the closest I found was this but AFAIK it is not the same) I have $r$ coins that land heads w.p. $p$. I want at least $m$ heads....
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### Markov Chain with heterogeneous transitions

I have a Markov chain as follows: $G+1$ finite states, it begins from $s=G$ and completes at $s=0$ A transition ($s\to s-1$) occurs in case if event $A$ happens. No other form of transition is ...
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### Conditional probability problem of three choices [duplicate]

I have the following problem where I have difficulties grasping the intuition: Lets say we have three boxes, with two of them empty and one containing a gold price. Lets say we randomly select ...
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### How many people could be wrong in telling a coin? [closed]

If we have two coins of radius of $R_1=8$ and $R_2=12$. Assume that 99% of people will be able to tell the size within $\pm5\%$ by touch it only, and assume it is a normal distribution. Question A: ...
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### Calculating $P(X=Y)$ for geometrically distributed random variables [closed]

I want to calculate $P(X=Y)$, where $X,Y$ are independent and geometrically distributed, which means: $P(X=k) = P(Y=k) = p(1-p)^k$, $k \in \mathbb N_0$ and $p \in (0,1)$. Can anybody tell me how to ...
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### Probability of infinite intersection.

I came to the following problem: Let $A_1, A_2, ...$ be events in a probability space $(\Omega, F, \mathbb{P})$ and $\mathbb{P}[A_j]=1$ for all $j>1$. I need to show that the probability of the ...
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### Expected number of draws to get n number of one object

I have been playing a game and came up with this question: There are $n$ different object, and each time you randomly choose one of them. One success is defined as one of the objects being selected ...
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### Expected number of trials until first success

I am trying to calculate the expected number of attempts to obtain a character in a game. The way the game works is there is a certain probability in order to capture the character. Given that you ...
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### Using Lindeberg’s Condition together with the Central Limit Theorem

I have the following problem: Problem. Let $(X_{n})_{n \in \mathbb{N}}$ be a sequence of independent random variables such that  \mathbf{Pr} \! \left( X_{n} = \sqrt{n} + 1 \right) = \...