Mathematics Stack Exchange
Mathematics Stack Exchange

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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Biased coin with a $3/4$ chance to land on the side it was before the flip

Consider a hypothetical coin (with two sides: heads and tails) that has a $3/4$ probability of landing on the side it was before the flip (meaning, if I flip it starting heads-up, then it will have an only $1/4$ probability of landing tails-up). If…
Seth Wyma
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Accounting for uncertainty in an Elo rating system for Foosball

For a Foosball game at work we implemented a rating system based on the Elo system. Allthough we achieved a sensible result so far, which provided us with a lot of fun (which is the goal) we feel we can do better by: accounting for uncertainty for…
Alex Kamphuis
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Probability that at least one of the bullets will go on forever.

There's a gun located on an infinite line, let's say at 0 on number line. It starts shooting bullets along that line, +X axis, at the rate of one bullet per second. Each bullet has a velocity in the range [0, 1] m/s randomly chosen from a uniform…
ABcDexter
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Estimating maximum value of random variable

Suppose I have some random variable $X$ which only takes on values over some finite region of the real line, and I want to estimate the maximum value of this random variable. Obviously one crude method is to take many measurements, lets say $X_1$,…
tom
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Help provide a proof of the Helly–Bray theorem

Given a probability space $(\Omega,\cal F, \Bbb P)$, the distribution function of a random variable $X$ is defined as $F(x)=\Bbb P\{X \le x\}$. Now if $F_1,F_2,...,F_{\infty}$ are distribution functions, then the question is Is $F_n…
Tony
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Solitaire probability

I would like to know the exact probability of the following game. I start counting from one to 13 and do this totally four times. On each turn I say a number and turn a card from a deck. Ace is considered to be as 1. If on one turn I say the same…
layman
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The likelihood of being an accountant vs being an accountant and a plumber

This is a very interesting word problem that I came across in an old textbook of mine. So I know it's got something to do with probability, but other than that, the textbook gave no hints really and I'm really not sure about how to approach it.…
anonymous
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Basic probability: Romeo and Juliette meet for a date.

Romeo and Juliet have a date at a given time, and each will arrive at the meeting place with a delay between 0 and 1 hour, with all pairs of delays being equally likely. The first to arrive will wait for 15 minutes and will leave if the other has…
TheUltravioletCatastrophe
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Inter-causal reasoning: How to solve probability with two conditions?

Below is the scheme of conditional dependence and the probabilities of events: P(A=1) = 0.01 P(A=0) = 0.99 P(B=1) = 0.1 P(B=0) = 0.9 P(C=1|A=0,B=0) = 0.1 P(C=1|A=0,B=1) = 0.5 P(C=1|A=1,B=0) = 0.6 P(C=1|A=1,B=1) = 0.9 Given the probabilities above…
niko
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Can the probability of an event be an irrational number?

I am wondering whether it is possible to construct an experiment, where the probability of occurrence of an event comes out to be an irrational number.
Nemo
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double decker, 13 card flush vs. 18+ of each color card. Who has the better odds of winning?

Two people, call them $A$ and $B$, decide to play a card game. They take 2 standard decks of playing cards and combine them into a "superdeck" of 104 cards, shuffle them well, and then draw 1 card at a time randomly without replacement. $A$…
David
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Linearity of expectation for infinite sums?

I have a question related to this post: Expected value of infinite sum Is the condition listed necessary/sufficient (or both?) For instance, I'm thinking of $X_n=\frac{1}{n}Z_n$, where $Z_n \sim$N(0,1) are iid. It "feels like" $E\sum_{n=1}^\infty…
Jason
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Joint distribution of $\min(X_1,\ldots,X_n)$ and $\max(X_1,\ldots,X_n)$.

Let $X_1,\ldots,X_n$ be independent random variables with common cumulative distribution function $F$. I am trying to find the joint cumulative distribution function of $$U=\min(X_1,\ldots,X_n)\quad\text{and}\quad V=\max(X_1,\ldots,X_n).$$ The…
Flower
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Conditional probability that a rotated inner product is zero

Consider a two random vectors $v=v_1,\dots, v_n$ and $w=w_1,\dots, w_n$, each of $n$ elements, each of which is independently $\pm1$ with prob $1/2$ . Let $n$ be even and let $X$ be the inner product of $v$ and $w$. We know: $$P(X = 0) = {n…
user138491
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What's the probability of a an outcome after N trials, if you stop trying once you're "successful"?

This follows on from this question about being hit by a bus. In this question, there is a 1/1000 chance of being hit and the question was about the probability of being hit if you cross the road 1000 time. I wondered what would happen to this…
Dancrumb
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