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 of tournament never ending

Three players $A,B,C$ play tennis matches. There is always one player waiting to face the winner of the match between the other two. For a given match both players have the same probability of winning. The tournament ends whenever a player wins two…
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A probability problem about picking balls - and somehow related to solar panels

CONTEXT Hello everyone! I decided to make this post for a friend of mine, who is currently working on energy-related subjects. She had been asked to simulate how solar panels would react when being randomly damaged. She was able to complete this…
Jujustum
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A question in Stochastic Convergence

I was reading a proof in a paper and got stuck at the following. Have been trying by best to figure this out for a long time but had no luck. It says: When we…
John
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Ball color expected value

We have a box containing b black balls and r red balls which we will take out one at a time by placing them on the table in front of us. Before each extraction we write the color of the majority of the balls not yet extracted on a sheet of paper and…
Monster
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Please help on this Probability problem

A bag contains 5 red marbles and 7 green marbles. Two marbles are drawn randomly one at a time, and without replacement. Find the probability of picking a red and a green, without order. This is how I attempted the question: I first go…
Sylvester
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Random variable independent of itself

Could someone help me find a way out: If $X$ is a random variable and $X$ is independent of itself. Show that there is a constant $a$ such that $P(X=a)=1$ if and only if $E[X_1]$ exists.
Zico
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Given a list of numbers, probability of the first number being the maximum?

So I'm traversing this trivia book which has a question that has intrigued and widely confused me. 1.) Since we have $n$ number of elements, then the probability of it being the largest among the $n$ choices is $\frac{1}{n}$, which seems…
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Probability for getting $n$ black balls

In a jar there are $ 5 $ white and $ 7 $ black balls. each time we choose a ball, it is returned with addition of two balls in the same color.Find the probability that the n first chosen balls are black. For 2 balls the probability is…
user65985
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Probability of winning with $\{1,\dots,9\}$ vs $\{1,\dots,8\}$

Assume A and B have access to the set $\{1,\dots,9\}$ and $\{1,\dots,8\}$, respectively. They choose three numbers from each's set without replacement and form the largest 3-digit number accordingly. For example, 4,2,5 means 542. What's the…
WWSS
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Independence of sums of gaussian random variables

Say, I have independent gaussian random variables $t1, t2, t3, t4, t5$ and I have two new random variables $S = t1 + t2 - t3$ and $K = t3 + t4$. Are $S$ and $K$ independent or is there any theorem about independece of random variables formed by sum…
key
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Show that $E(|X-a|) = \int_{-\infty}^a P(X < x) \, dx + \int_a^\infty P(X > x) \, dx$

How to show: $E(|X-a|) = \int_{-\infty}^a P(X < x) \, dx + \int_a^\infty P(X > x) \, dx$. I have: $$E(|X-a|) = \int |X-a| \, dP = \int_{\mathbb{R}} |x-a| P_X(dx) = \int_{(-\infty,a)} a-x P_X(dx) + \int_{(a,\infty)} x-a P_X(dx)$$ But I do not see…
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Say I have a bag of 100 unique marbles. With I replacement, I pick 10 marbles at a time, at random.

Say I have a bag of 100 unique marbles. With replacement, I pick 10 marbles at a time, at random. How many times will I have to pick the marbles (10 marbles a pick) in order to have a 95% chance of having seen every unique marble at least once.
David
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Help with understanding and studying probability

I'm a CS major and self studying sheldon ross's first course in probability book, before that I have taken a calculus based probability course, not a strong one, which ended with superficially covering content in ross's 6th and 7th chapter. We…
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How to calculate the probability or 50% or more matches on n randomly assigned unique pairs

FTR: This could not be a lower priority question. It's so not important, but I really want to know. Let's say I have n unique pairs. They are like keys (A) and locks (B), and every one of the n locks can be opened by exactly one of the n keys. And,…