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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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How many rounds does it take to be 99% sure of reaching Expected Value?

I have a feeling this might be a common question but I was unable to find the right way of asking, and I'm just a hobbyist at stats/math. Say I have a bet that costs six dollars. If I lose I get nothing, and if I win I get my six dollars back, plus…
tunesmith
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Having difficulty understanding probabilities in this question

Question: Given $5$ people in an elevator on the ground floor, and the buttons for the second, third, and forth floors are lit, what is the probability that two people will exit the elevator at floor $3$? Maths noob here. I have spent about $10$…
tom redfern
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Expectation of an exponential function

Why is the expectation of an exponential function: $$\mathbb{E}[\exp(A x)] = \exp((1/2) A^2)\,?$$ I am struggling to find references that shows this, can anyone help me please? If anyone could enlighten me it would be great!
Damian
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Does $Var(X^2) \geq (VarX)^2$ hold?

It is well known that $E(X^2) \geq (EX)^2$, but I was wondering if there is a similar result for variances, e.g. is $Var(X^2) \geq (VarX)^2$? I was doing some research and came up with that inequality, but I can’t prove it. I’ve done simulations in…
Blaza
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Probability that no three consecutive heads occur

Suppose we flip a fair coin $n$ times, what is the probability that no three consecutive heads occur? I understand the proof for the case with no two consecutive heads, where we can consider the number of sequences that start with $H$ and $T$ and…
user513433
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Probability that distance between $X$ and $Y$ is $>$ $L/3$

Two points are selected randomly on a line of length $L$, so as to be on opposite sides of the midpoint of the line[In other words, the two points $X$ and $Y$ are independent random variables with a uniform distribution over $(0, L/2)$ and $(L/2,…
CAF
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Classic $2n$ people around a table problem

A total of $2n$ people, consisting of $n$ married couples, are randomly seated (all possible orderings being equally likely) at a round table. Let $C_i$ denote the event that the members of couple $i$ are seated next to each other, $i = 1,...,n$ a)…
CAF
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Poisson random variable is not sub gaussian

I am reading a chapter on concentration inequalities, and I am struggling to make connections on sub-Gaussian random variables. A random variable is sub-Gaussian if there exists $C > 0$ such that $P(|X| \geq t) \leq 2\exp(-t^2/C^2)$. The text…
user231
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Probability on circumference

Let $\xi$ be uniformly distributed on $\left[-\pi,\,\pi\right]$, $X = \cos \xi$, $Y = \sin \xi$. Is it true that $\Pr \left( X=1\mid Y=0 \right) = 0.5$? It is obvious this problem cannot be solved in term of events as $\Pr \left( Y=0 \right) = 0$.…
Denis Korzhenkov
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Probability of meeting

This is a basic probability question. Persons A and B decide to arrive and meet sometime between 7 and 8 pm. Whoever arrives first will wait for ten minutes for the other person. If the other person doesn't turn up inside ten minutes then the…
eddie
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probability problem in Binomial distribution

The question: A newsboy purchases papers at 12 cents and sells them at 16 cents. However, he is not allowed to return unsold papers. Suppose that his daily demand follows a Binomial distribution with n=10, p=1/3. His mother suggests him to…
user227158
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Probability problem (withdraw balls from the urn)

Problem: An urn contains 3 red and 7 black balls. Player A and B withdraw balls from the urn consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no…
Kes
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Conditional probability of cows

the question is that if you are a farmer and own six cows: 3 white, 2 black and one that is black on one side and white on the other. Then if you see two black cows (that is 2 black sides of cows) then what is the probability that one of them is the…
Ben
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How exactly is the probability of at least one event happening dependent on the probability of all events happening?

Say we have $P(A) = 0.60,\, P(B) = 0.50$ . Normally to find the probability of at least one happening, we find the probability of neither of them happening: $$P(A^c \cap B^c) = 0.40 \times 0.50 = 0.20$$ and then subtract it from $1$ ( getting…
Hello
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Probability of a survivor in chick-pecking tournament

This is a follow up to this question: Suppose that $n$ chicks are arranged in a circle. Every chick randomly pecks either the chick to their right or the chick to their left. By the other question, the expected number of unpecked chicks is $n/4$.…
John Coleman
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