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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: there are $n$ rooms, and $m$ meetings, $m \leq n$, what's the probability of all meetings scheduled to a different room

Quite new in stats... definitely not my strong area. I came across this probability question, and I am not sure how to do this! The question goes: pretend that there's this meeting scheduling engine used by this company and is not synced in…
alwaysaskingquestions
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How to compute $E[\log(X)]$ when $X$ follows a beta distribution?

Given a Beta variable $X \sim B(\alpha\ge 2,\beta)$, how do I compute the expectation of its logarithm $E[\log(X)]$? This is deemed "obvious" on MO, but I see no easy way to compute $\int_0^1 x^{\alpha-1}(1-x)^{\beta-1}\log x \; dx$. Differentiating…
sds
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Probability of one event given the probability of two other events

Let $A$, $B$, and $C$ be events. Suppose $P(A) \ge .9$, $P(B) \ge .8$, and $P(A \cap B \cap C)=0$. Show that $P(C) \le .3$. Now, I tried using the inclusion-exclusion principle to solve this, but I'm getting nowhere. Perhaps that is the correct way…
mamyot0
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Binomial or Uniform Probability?

What is the probability of rolling exactly two sixes in $7$ rolls of a die? I know this is a binomial probability. $P(X=2)=\binom{7}{2}(1/6)^2(5/6)^5$. By the definition of probability formula "Probability formula is the ratio of number of favorable…
user81411
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Risk and Die-Rolling Probabilities

If you aren't familiar with Risk, here is a short description of how the game works: In the game of Risk, players control countries by occupying them with a variable number of “armies.” The object is to gain more territory by conducting battles…
Demetri Pananos
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If $A$ is independent of $B$ and $C$ then why is it not necessarally independent of $B\cap C$?

I'm attempting to acquire an intuitive understanding of why the content in the question of the title is correct, however I am unable to do so. Is there way of thinking about the result that makes sense? …
David
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About the Moment Generating Function

Let $X \sim \exp(\lambda)$. Prove that : $E[X^n] = n!/\lambda n$ The hint in (Fundamentals of probability) gives the hint use the Moment Generating Function, but I can't see how I should use that to prove that this is the respective expression that…
Junior Eshun
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probability of events after a number of tries

Suppose a player is playing a game and killing a monster, and the likelihood of a monster dropping an item is given by some probability p. The player would like to know the probability of getting $\bf{exactly}$ n of these drops in m kills. My…
user225028
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Possible combinations for 20 character alphanumeric identifier

I need to know the total possible unique variations there can be on an identifier that is made up of 20 alphanumeric characters, where the characters are A to Z (all upper case), and the digits 0 to 9.
John
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What are the odds of winning this bingo game?

I'll explain the game real quick, it's called Pick 8. You get a sheet of paper, containing 3 rows of 8 boxes. You fill out each row with numbers 1-75, in any order, with no duplicates. The bingo caller then starts calling bingo numbers. If you get a…
Steven
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Suspect unfair die

If I claim to have a fair die that rolls 1-6 uniformly but my die actually only rolls 1-5 uniformly (and never produces a 6) how many rolls would you need to see before you had over 50% confidence that I was messing with you?
candied_orange
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Joint distribution between sum and a component of its sum

Let $X$ and $N$ be independent uniform random variables on $[0,1]$. Define, \begin{equation} Y=X+N \end{equation} I am interested in computing the joint distribution $P_{XY}$. I have the following tried from my side.…
Dinesh
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why scale a normal distribution by the square root of the variance?

Given a standard normal distribution $N(0,1)$ why, if you wish to scale it, you need to multiply by the square root of the variance? Ie given a variance t, the new scaled distribution is $N(0, t)$ which is equivalent to $\sqrt{t}*N(0,1)$? Isn't the…
shoestringfries
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What's the probability that I will earn \$25?

I go to a casino with \$100. At the casino, I play a game in which I get \$1 if I win, and lose \$1 if I lose. The probability of me winning is $\frac{1}{4}$, and I must either win or lose every time I play this game. I will keep playing this game…
David Faux
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Probability that a 5-card poker hand contains a flush or a three of a kind

Please excuse me if I don't type this right, this is my first posted question. I hope I do this right.... I'm having problems with a question from my Intro to Math Analysis course. It is not from any book, but a worksheet that the professor made…
dsfsu
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