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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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Multivariate Gaussian Definition when Covariance matrix is singular, What's wrong?

Given $$\mathbf{\Sigma} \in \mathbb R^{k \times k}$$ $$\mathbf{u} \in \mathbb R^k$$ The multivariate Gaussian pdf can be determined By…
Allen Kuo
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Probability that the last ball is white?

A jar contains $m=90$ white balls and $n=10$ red balls, the balls are drawn under the following constraints: the ball is thrown away if it is white; the ball is put back if it is red and another ball is drawn; this time, the ball is thrown away no…
Rock
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2 people on a random walk

Say you have a building of $HJ$ rooms, where $H$ and $J$ are positive integers (a rectangular grid of rooms of size $H$ times $J$). You can label the rooms $(h,j)$ where $1 \le h \le H$ and $1 \le j \le J$. One person enters the building of rooms at…
Patrick Da Silva
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Looking for intuition behind coin-flipping pattern expectation

I was discussing the following problem with my son: Suppose we start flipping a (fair) coin, and write down the sequence; for example it might come out HTTHTHHTTTTH.... I am interested in the expected number of flips to obtain a given pattern. For…
Fixee
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How to calculate the $4$th central moment of binomial distribution?

I just derived it by using the generation function to first get raw moments. The result is $(-1+3np^2-6p^2-3np+6p)n(p-1)p$. It was merely brutal force calculation, nothing interesting. So I was wondering, if there any one knows tricks that could…
NonalcoholicBeer
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Random ants probability question

500 ants are randomly put on a 1-foot string (independent uniform distribution for each ant between 0 and 1). Each ant randomly moves toward on end of the string (equal probability to the left or the right) at constant speed of 1 foot/minute until…
Jojo
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Probability of an event occuring at least once in 50 tries

Probability of an event is $.116$. In $50$ tries, what are the chances at least one event occurs? I see that the probability that it wouldn't happen in one try is $.884$ and the probability that it wouldn't happen in two tries is $(.884)^2$.
Jim
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Conditional probability given multiple independent events

I am interested in finding the conditional probability $P(A|E_1,E_2,...,E_n)$ where the $E_i$ are mutually independent events. I know only $P(A)$ and $P(A|E_i)$. Is this possible? If so, how? If not, what information is missing?
Anders
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deriving cdf of uniform distribution

I have that the pdf for a uniform distribution is given by $$f(x) = \frac{1}{b-a}$$ if $a \leq x \leq b $ and $0$ otherwise. I am trying to derive the cdf. From definition I have that the cdf is given by $F(x) = \int_{-\infty}^x f(t) \ dt$ So I will…
newmathsstudent3
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Probability of a double-headed coin

Here are three related problems from Blitzstein and Hwang's Introduction to Probability. Curious if my approach is sound. I'm reasonably confident in the first result, but not so much in the other two, particularly the last one. 1:: A hat contains…
user235080
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The expected area of a triangle formed by three points randomly chosen from the unit square

"Three points are chosen uniformly and at random from a unit square. What is the expected value of the area of the resulting triangle?" I need to do a research about that problem and i found this suggested solution: here. Now, I understand almost…
kitsuneFox
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On the number of consecutive tails when flipping a biased coin

Say we flip a biased coin such that the probability of getting the same outcome in a row (head-head or tail-tail) is $p$. What is the probability of getting three or more tails consecutively out of $n$ flips (and alternatively out of infinite…
Gizem
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Probability: People sitting in a row (linear arrangement)

Question: Ten persons are seated at random in a row. What is the probability that a particular couple will be seated together? My attempt: 9! 2!/ 10! = $\dfrac{1}{5}$ , since there are 9! ways of sitting in pairs and 2! ways to arrange a couple.…
Eddie
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Probability of winning a game in tennis?

Suppose there is a tennis singles match, where Player A plays a single game against Player B. The probability that player A will win a single point is $x$, and thus $1-x$ is the probability that Player B will win a point. The scoring system in…
Kenshin
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Probability of Sets

I need some help on this one: We have sets $X$ and $Y$ chosen independently and uniformly at random from among all subsets of $\{1,2,\ldots,100\}$. Determine the probability that $X$ is a subset of $Y$.
Tom chan
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