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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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probability distribution of X+Y

Let a fair die be rolled 2 times. The 2 rolls are independent. Let X and Y be the outcomes of the first and second rolls, respectively. a. What is the probability distribution of X+Y? What is each unique possible value of X+Y and each possibility’s…
Anna
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Find E(XY) and covariance

I am given n independent Bernoulli trials, prob success = p. If X is # of successes, and Y is the number of failures, what is E(XY) and Cov(X,Y)? I was trying to use E(XY) - E(X)E(Y), the second component is easy, but I can't think of an easy way of…
problab
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where are my calculations wrong? Expected value

I am given a pdf $f(x) = |x-1|$ for $0 \leq x \leq 2,$ 0 otherwise, and asked to find expected value of $X^{2} + X.$ I simply integrated $(x^{2} + x)|x-1|$ from 0 to 2, checked with mathematica, and got $\frac{5}{2}.$ The answer in the back of the…
pdfin
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Dividing colored balls between children

The following was an exercise I solved: We have 8 numbered balls - two blue, two red, two green, and two yellow. When dividing them between 4 children, 2 balls each, what is the probability at least one child will get two balls of the same…
roel
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Probability of defeating enemy (info on distributions added)

I have 27 hit points and my opponent has 50, and the winner is the player that reduces the other player's hit points to 0 first. My expected damage inflicted per round is 5. My expected damage taken per round is 7/3. I have the first attack. What…
Altheus the Unready
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Calculating Conditional Probability for Continuous Random Variables (Density Function or PDF)

Is that possible to calculate this? $$P(Y \leq \frac{1}{2} | X = 2)?$$ $X$ and $Y$ are both continuous random variables. I am asking this question because I know that we can't calculate a density function in a point, instead we should specify an…
Arya
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Distribution of Functions of Random Variables

In general, how would one find the distribution of $f(X)$ where $X$ is a random variable? Or consider the inverse problem of finding the distribution of $X$ given the distribution of $f(X)$. For example, what is the distribution of $\max(X_1, X_2,…
NebulousReveal
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covariance of increasing functions

Suppose $f$ and $g$ are monotonically increasing, and bounded, and let $X$ be a random variable. I want to show $f$, $g$ have positive covariance. I tried to compute it directly but I am not getting anything useful
cori
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Choosing the correct combinatorial method

A box contains 24 lightbulbs 2 of which are defective. If a person selects 10 lightbulbs at random without replacement, what is the probability that both defective bulbs will be selected? I'm searching for the right way to select the sample…
upabove
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Expected number of intersection points when $n$ random chords are drawn in a circle

There are $n$ random chords drawn in a circle. I am trying to determine the expected number of points in which the chords intersect within the circle.
KenG
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Drawing a ball question

Suppose we draw 3 balls without replacement from an urn with 2 red, 2 green, and 2 blue balls. How can I find the probability of each 0 red, 1 red and 2 red? I know the number of sample space is 120 ( Since we draw 3 balls and 6 balls in total, it…
David Taeyang Lee
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$A$ and $B$ are events, is $A|B$ an event?

$A$ and $B$ are events, is $A|B$ an event? Can I write an event in this form $A|B$ ? $Pr(A|B)$ means given $B$ happens, what is the probability of $A$ happen. Since $Pr(\cdot)$ is a measurement, so I am wondering $A|B$ is an event too
lulu
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Probability of getting $4$ smallest Balls in $2$ Boxes

I have $2n$ balls labeled $1, 2, \ldots, 2n$, and two boxes, Box $1$ and Box $2$. I take $n$ of the balls at random without replacement and place them in the Box $1$. I take the remaining $n$ balls and place them in the Box $2$. I take the two…
caligirl11
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If I flip a coin $100$ times, why do the results trend towards $50-50$?

This sounds like a simple question, but here's the gist: Given a coin flip (or some other random process that can result in one of two outcomes) that has a perfect $50-50$ probability of landing on heads or tails (the probability of heads is $50\%$,…
communistpancake
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Is there a mistake in this question?

For a random variable $X$ with mean $\mu$ and variance $\sigma^2$ define $V(x)=\mathbb{E}(X-x)^2$. By expressing $V(X)$ in terms of $\mu,\;\sigma^2,X$ show that $\sigma^2=\frac{1}{2}\mathbb{E}(V(X))$. My question is: isn't $V(X)=0?$ I've…
simon
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