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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Probability Question about Tennis Games!

$2^{n}$ players enter a single elimination tennis tournament. You can assume that the players are of equal ability. Find the probability that two particular players meet each other in the tournament. I could't make a serious attempt on the…
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Probability question with a deck of cards

Just started to learn maths, so I'm sorry if this an elementary question. The question is: here is a deck with 40 cards ; 10 cards, each 10 with one of the 4 shapes (hearts, diamonds, clubs and spades). All the cards are numbered from 1 to 10. Every…
Yoxbox
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Can we treat these events as independent?

Problem: The chances of someone having a genetic stigma is $1$%. Assume a couple with $2$ children. If both parent have a stigma, the chances of each child having it is $50$%. If just one parent has a genetic stigma, the chances of each child having…
Than1
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Ball drawn with replacement - with a twist. Is there an elegant solution I may be missing?

Here's the question: Suppose there's a bag filled with balls numbered one through fifty. You reach in and grab three at random, put them to the side, and then replace the ones you took so that the bag is once again filled with fifty distinctly…
Jotak
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How to obtain tail bounds for a sum of dependent and bounded random variables?

Note: I divide this question to two separated question not to be duplicate version. I am looking for tail bounds (preferably exponential) for the sum of dependent and bounded random variables. Consider $$K_{ij}=\sum_{r=1}^N\sum_{c=1}^N…
Farzad
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Distribution of dot product?

What is the distribution of the random variable $$X = a \cdot b$$ where $a, b$ are unit $m$-vectors independently drawn from the uniform distribution on the unit $m$-sphere? Is there a special name for this distribution? EDIT: Thanks to Joriki for…
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Demonstrating a coin is not fair with as few flips as possible

Suppose you have an "unfair" coin, that lands heads with probability $p\in(1/2,1]$ (where $p$ is known to you). You are given some $\epsilon>0$, and want to demonstrate to someone that this coin is not fair with confidence $1-\epsilon$, using as few…
Julian Rosen
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Probability, integers and reals (soft question)

Given a random integer, is the probability of correctly guessing what it is exactly zero? What if it would be a real number, rather than an integer? Does the fact that the set of all integers is countable and the set of real numbers is uncountable…
Constantine
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Doubt about Probability Question

There is a box containing $20$ green marbles, $20$ blue marbles, and $20$ purple marbles. You draw $10$ marbles at random without replacement. What is the probability that you do not get all the colors? The solution in the book: $\Large…
john
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The triangle inequality holds... $50\%$ of the time? Or is this problem asking for something else?

Here's a question from my probability textbook: If three numbers be named at random it is just as likely as not that every two of them will be greater than the third. I don't understand what this problem is even asking, it's not clear what this…
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Average number of heads in filtered coin toss

I have a coin that, when tossed, produces heads with probability $p \geq 0.5$ and tails with probability $1-p$. I start a coin-tossing experiment. Whenever I get more than one tail in a row, I discard the second tail and toss again, so that my…
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Does the probability of team A winning a series of seven games depend on whether team A plays until they win the four games needed or all seven?

In the World Series of baseball, two teams (call them A and B) play a sequence of games against each other, and the first team to win four games wins the series. Let p be the probability that A wins an individual game, and assume that the games are…
beginner
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Nine person of equal strength playing in tournament

Nine persons $P_i$ , i = 1, 2, ...., 9 of equal strength are playing a tournament such that they are first grouped in to three groups A, B, C each containing three persons at random and a winner from each group is selected and. a new group is formed…
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Number of times you can play a game in an hour?

Suppose that you have a game you can play that takes a variable amount of time to finish - suppose it takes between $A$ seconds and $B$ seconds to complete, and is uniformly distributed between the two. Given $A$ and $B$, is there an easy way to…
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$X \sim U [-0.5 , 1.5] , Y = X^2$

Given $$ f(x) = \begin{cases} \frac12 &,\ -0.5 \le x\le 1.5\\0 &,\ \mbox{otherwise} \end{cases}$$ find the probability density function of $Y=X^2$. To solve this I first divided up the pdf of X into three parts: $$f(x) = \begin{cases} \frac12 &, \…
Ben
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