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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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When does pairwise independence imply independence?

We know if a collection of events are independent, then they are pairwise independent. In general, the converse is not true. However, I'm wondering if there's a condition under which the converse holds. I haven't been able to find anything on this.…
epsilon-delta
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How many players needed for the game to have the highest probability of finishing the fastest?

Welcome to the fictional game of "color-tag"; the not-so-fast-paced cousin of paintball Where marking your opponent is all that counts! If $A$ marks $B$ with his/her color, then $B$ will be permanently marked with $A$'s color, but at the same time…
JohnWO
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What is the probability that I roll a 2 before I roll two odd numbers?

Assuming that I use a standard die, what is the probability that I roll a 2 before I roll two odd numbers? The odd numbers do not have to be distinct. For example, 1,6,4,2 wins and 3,3 loses.
heyhuehei
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Distribution of the maximum of $n$ uniform random variables

If $U_1,\dots, U_n$ are independent uniform random variables with range $\{1,\dots,N\}$, what can be said about the distribution of $Z=\max U_i$? I am interested in the case where $n$ is large and $N\geq n$. In particular, I am interested in tail…
user66307
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Is the variance of a sum of infinitely many independent random variables the sum of their variances?

For $X_i$ independent, is $\operatorname{Var}\left(\sum \limits_{i = 0}^\infty X_i \right) = \sum\limits_{i=0}^\infty \operatorname{Var}(X_i)$? Thanks!
badatmath
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Is this a correct Monte-Carlo expression for $\pi$?

I have a bicycle with one of those O-locks on it and too often when I park the bike and I want to lock it, the lock hits one of the spokes of the rim. This can be frustrating and surprises me that it occurs so often. I mean, the spokes are so thin…
Physics_maths
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Why is it that $E(xy) = E(x)E(y)$ if $x$ and $y$ are uncorrelated random variables?

Also, why does $E(xy) = E(x)E(y)$ not hold if $x$ and $y$ are correlated? Perhaps at a more basic, intuitive level, what's the difference between $E(xy)$ and $E(x)E(y)$?
David Faux
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Can the Poisson Distribution be used to find the expected value of time of arrival given an expected arrivals per unit time?

My understanding of the Poisson Distribution is that its PMF $P(x=k) = \dfrac {\lambda^k e^{-\lambda}} {k!}$ refers to the probability of finding k events given an expected arrival expectancy $\lambda$. This gives me, rather trivially, that the…
Teofrostus
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Probability question: $100$ balls with $r$ red balls.

Queation:A box contains 100 balls, of which r are red. Suppose that the balls are drawn from the box one at a time, at random, without replacement. Determine (a) the probability that the first ball drawn will be red; (b)the probability that the…
Silent
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What are the chances of finding all the balls?

Given $x$ distinguishable balls (say they have different colors), sample with replacement repeatedly until all the balls that have been sampled have been sampled at least twice. I am interested in $$P(\text{number of distinct balls sampled} =…
Simd
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Sending a message in bit form, calculate the chance that the message is in its original form after transfer

A message consists of 100 bits (either 0 or 1), of which every bit can change (from 0 to 1 or the other way around) during the data transfer with probability p = 0,001 (independently of other bits). What is the probability that a message is in its…
Noolenne
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Independent events or conditional probability?

In my daily morning walk there is a 20% chance I drop my pouch. Every day I follow the exact same straight path, to the district square and then back. Assuming that my walk is on a straight segment from A to B and then back from B to A, what is the…
Eduardo Juan Ramirez
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Probability of getting 'k' heads with 'n' coins

This is an interview question.( http://www.geeksforgeeks.org/directi-interview-set-1/) Given $n$ biased coins, with each coin giving heads with probability $P_i$, find the probability that on tossing the $n$ coins you will obtain exactly $k$ heads.…
Kyuubi
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Probability that there exists a person who will "only flip heads" or "only flip tails" in their lifetime?

My question has two parts: Am I approaching the problem correctly, resulting in a reasonable formula? How do I do the final calculation for numbers as large and as small as these. I put my formula into google and it just gives an answer of "1",…
user1937279
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$E[|X-\mu|^n] \le 2 E[|X-\mu|^{n+1}]$ for Integer Random Variables

I would like to prove the following moment inequality for all integer random variables ($X\in\mathbb Z$) for which the $n+1$th moment is defined: $$\mathrm{E}[|X-\mu|^n] \le 2 \mathrm E[|X-\mu|^{n+1}].$$ ($n\ge1$, but probably doesn't have to be an…
Thomas Ahle
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