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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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What’s the probability for this problem?

in class we were working on a question regarding our seating plan. The question was: we are a class of 32 students sitting in pairs of 2. What is the probability of one or more pairs existing in an original seating plan and after shuffling all…
kian
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Is $A \vert B$ an event, or is $P(A \vert B)$ an abuse of notation?

Suppose we have a probability space $(\Omega, \mathcal{F}, P)$. Thus, when we write $P(A \vert B)$, either $A \vert B$ is an element of the event space $\mathcal{F}$ (i.e. the domain of $P$), or this an abuse of notation. I suspect that this is…
William Lewis
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Understanding the Likelihood Principle - What is the Big Deal here?

I am reading about the Likelihood Principle (https://en.wikipedia.org/wiki/Likelihood_principle). In short, I think the Likelihood Principle discusses the phenomena that if two experiments have the same underlying likelihood function, then even if…
stats_noob
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Probability of drawing an Ace: before and after

this is my first question on the website. When I took probability, one of the first questions in my textbook was this: What is the probability of drawing an ace in a standard 52-card deck? That one was pretty easy, thankfully. The next one threw…
mathmath8128
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Probability of Drawing a Particular set of Cards from a Deck

I think this is a pretty simple question. If I've got a deck composed of the following cards: 4x Red, 2x Green, 4x Blue, 8x Orange, 3x Purple What is the probability, after drawing 5 cards, that there will be at least 1 Red card and 1 Green card?
Tyler Murry
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A model inspired by Plants vs. Zombies: What is the expected value of damage dealt by a Kernel-Pult when a zombie walks one step?

Here is an interesting model inspired by the game Plants vs. Zombies. A Kernel-Pult can lob either a kernel (with probability $1 - p$, dealing $1$ damage) or a butter (with probability $p$, dealing $2$ damage with stunning effect) to a zombie. (The…
lhy7889678
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Does the Central Limit Theorem Work for a Single Sample?

This is a question that I am struggling to understand. Suppose there is a university with 100,000 students (population) I take a sample of 100 students and measure the height of each student Then, I take the average height of these 100…
stats_noob
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Conditional density of Sum of two independent and continuous random variables

Let X and Y be independent and continuous random variables. How do you solve for the conditional density of X+Y given X
dyuta
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Probability in Pokémon Speedrunning

Background Hey folks. So I am, in addition to being a casual math and physics nerd, a Pokémon speedrunner. I run the game Pokémon Red Version and the category "Any % Glitchless (Classic)." For those of you who don't know speedrunning terminology,…
Adam Gluntz
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Probability of winning a match given probability of winning a game

If a team has probability p of winning each game, and if the team wins/loses a match when it is 2 games ahead/behind the other team, is there an analytical formula or approximation for the probability that the team wins the match, as a function of…
Fortranner
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Expanding a Probability Tree

Consider the following situation: Take some integer $N$ Each day there is a: $p_1$ probability that $N$ will increase by $n_1$ % of its current value $p_2$ probability that $N$ will decrease by $n_2$ % of its current value $p_3 = 1- p_1+ p_2$…
stats_noob
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Comparing the Sample Variance with the Population Variance

I read in the following paper (https://iopscience.iop.org/article/10.1088/0026-1394/41/3/004/pdf) on page 133 "The conditional standard deviation (...) is necessarily an underestimate of its unconditional standard deviation." . I am trying to…
stats_noob
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Expected value for $a^x$

Assume a random variable $X$. Assume, if this simplifies the problem, that $X$ can take only non negative integer values. Does there exist any relation between $E(X)$ and $E(a^X)$, where $a$ is an arbitrary value in the interval $[0,1]$ and by $a^X$…
Sim
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Number of Draws Needed to Win a Raffle

I was at a summer bbq picnic on the weekend and there was a raffle draw. There were different prizes on the table. Everyone had a ticket and they would randomly pick tickets - when a ticket was called, the recipient would come and pick up their…
Matthew
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Which indicator variable best predicts a sampled value?

There are two players in this cooperative game. I will first describe the basic game and then the real problem. Consider first that player 1 is to sample a single value from a standard normal distribution. Player 2 knows the distribution player 1…
Simd
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