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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 .

105859 questions
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Expected value of the minimum with limited independence

Imagine you sample $n$ number with replacement uniformly from the integers $1,\dots, n$. Let $X$ be the minimum of these samples. I am interested in $\mathbb{E}(X)$ but with a twist. All I know is that the samples are uniform and pairwise…
user66307
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Videogame (Dota 2) probability

In Dota 2 after you launch a spell you usually have a cooldown time you need to wait before being able to launch that spell again. In the Year Beast Brawl anyway powerful beasts can have Refresher Aura: Refresher Aura: When an allied hero casts a…
gyosko
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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 capture the character, there is now another…
tlw613sp
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Conditioning on a continuous random variable

I have a random variable $N(a)$, which depends on a number $a$, having the property that for all $a \in \mathbb{R}$, $$P(N(a) \geq 1) = p $$ The example I have in mind is $N(a)$ is $T-a$ where $T$ the time of first arrival in a Poisson process after…
Yuki L.
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Probability that product of any four natural numbers is divisible by 5

Given any four randomly chosen natural numbers (not mentioned if the numbers taken are distinct or not) what is the probability that their product is divisible by 5? My answers: The numbers chosen will either be of the form $5k$ or $5k+1$ or $5k+2$…
humble
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Prove that the probability of two event sets are equal

Consider this problem: Let $A_1, A_2,...$ be an arbitrary finite sequence of events. Let $B_1, B_2,...$ be another finite sequence of events defined as follows: $B_1 = A_1, B_2 = A^c_1 >\cap A_2, B_3 = A^c_1 \cap A^c_2 \cap A_3,.. $ Prove:…
blockR
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$n$ players throw a die and get score for each pair who throw the same number

Each member of a group and $n$ players roll a fair die. For every pair of players who throw the same number, the group scores 1 point. Find the mean and variance of the total score of the group. Here is what I tried: Let $S_i$ denote the score…
user120005
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Biased coin probability, uneven probability

Getting at least $2$ heads when flipping a coin $3$ times but the coin is biased so that heads are $3$ times more likely than tails. Can anyone explain how uneven probability works? Thank you
Stupid
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Odds of anyone in a group getting picked twice in a row

I'm going to make this question a little generic, but it's for a specific situation: You have a list of 10,000 people. Every week, you randomly select 2% (200) of those people. What are the odds of one or more of those 2% getting picked the…
Pete
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Why is it that shuffling a deck so that all permutations are equally likely requires swapping only later elements?

Apparently, to shuffle a deck of cards so that all permutations are equally can be done by going through the deck in order and swapping the current card with cards that do not appear earlier than the current card. Also apparently, if one just…
David Faux
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Calculating probability of getting $m$ unique numbers when choosing $n$ times from $0\ldots k$

I'm trying to write a test to verify a reasonable distribution for a function that generates 4-digit pin numbers from 8 digit phone numbers. I'm not aware of any direct method of calculating this, so my approach is to (1) generate $n$ pin numbers,…
thebjorn
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How to solve probability circular table problem with neighbors.

7 people are seated around a round table eating dinner. They then all get up, get dessert and then sit down at random. What is the probability that each person has two new neighbors? What is the answer to this question if there are 8 people? How…
user200614
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Probability of last person taking his own card

I was asked this question this time at lunch and could not stop thinking about it since then. I could not find the answer, so that's why I am asking here. The story is as following: n people write their name on a card and put it in a box. After…
Mike Voets
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Poisson distribution process

Meteorites hit the surface of the moon, treat as an infinite plane. The meteorites that have hit the moon over the last 1 million yrs can be modeled as a Poisson process with constant intensity lambda. Suppose that each meteorite leaves a…
James R.
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Prove the probability to even number of "Heads" is $\frac{1}{2}$.

Let $n$ coins, where at least one of them is a fair coin. Each one of the $n$ coins is tossed - Prove the probability to get even number of "Heads" is $\frac{1}{2}$. I'd be glad for a direction. Thanks.
AlonAlon
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