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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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Probability and Expectation People in Line

A group of n people all have distinct heights. They are waiting in a straight line at the bank (one person in front of the other), with all orderings of the people equally likely. A person can see ahead to the front of the line if they are taller…
Dee Chantelle
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Basic Approach To Independence In Probability

If we have an event $A$ and a sample space $\Omega$, can we say that the event $A$ is Independent on an event $B$ if the occurrence of $B$ keep the ratio of $\frac{|A|}{|\Omega|}$? For example: looking at a deck of cards, P(heart)=$\frac{13}{52}$…
gbox
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Conditional Probability for Exponential Random Variables

I'm working through a practice problem for an exam and I would like to verify that I've done it correctly. Additionally I'd like some insight on the intuition behind the numbers I'm getting. Problem For $X$ and $Y$ independent $Exp(1)$ r.v.'s…
probtheory
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Dice Roll Probabilities

I'm trying to figure out the probabilities for the following casino game: You and the dealer each roll a pair of dice and the person with the highest individual die roll wins. If its a tie, you win. First, what is the probability you win? Second,…
user3168139
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What are the odds that the pattern, win lose lose, will happen 23 times in a row (69 rounds)?

In a game of 50/50 (this example could be a coin flip). Before any flips, What are the odds that the pattern win lose lose (heads tails tails if your choice was heads each time.) will happen 23 times in a row (69 rounds)? What about after the chain…
UhlBelk
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Find a pdf of a function of a random variable

Let $Y$ be an exponential random variable with parameter $\frac12$. Let $X=e^{-Y/2}$. Determine the pdf of $X$. $$f(t)=\frac{d}{dt}P(X\le t)=\frac{d}{dt}P(e^{-Y/2}\le t)\\=\frac{d}{dt}P(Y\ge-2\ln t)=\frac{d}{dt}(1-P(Y<-2\ln t))=-\frac12e^{\ln…
matkis
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Question about the independence definition.

Why does the independence definition requires that every subfamily of events $A_1,A_2,\ldots,A_n$ satisfies $P(A_{i1}\cap \cdots \cap A_{ik})=\prod_j P(A_{ij})$ where $i_1 < i_2 < \cdots < i_n$ and $j < n$. My doubt arose from this: Suppose…
Rodolfo
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Problems with this reasoning (Gambling)

Some mate of mine is some casino lover, and he usually says something like this to justify his hobby. "Let's suppose we have a game, in which I gamble something, and if I win, I receive the double, and if I lose I don't receive anything. So I gamble…
Nell
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A continuous analogue of the binomial distribution

For any positive integer $N$, the binomial$(N!,p)$ distribution has the following property: for any $1 \leq n \leq N$, there exist i.i.d. random variables $X_1,\ldots,X_n$ such that $X_1 + \cdots + X_n \sim {\rm binomial}(N!,p)$ (specifically, we…
Shai Covo
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Show that if $P(0 \leq X \leq c)=1$ then $Var(X) \leq \frac{c^2}{4}$

I need to show that if $$P(0 \leq X \leq c)=1$$ then $$Var(X) \leq \frac{c^2}{4}$$ I can show that using 2 things: First, that $E[X^2] \leq cE[X]$ and secondly that $Var(X) \leq c^2[\alpha(1-\alpha)]$ for $\alpha=\frac{E[X]}{c}$. Could anyone help…
E Be
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what is the best way to win: every 1000 submission will win

I have a question about probability. The game is like this: Every $1000$th submission will win, but the players don't know how many submissions were made before. Is it better for a player to throw all of his $100$ credits in one time or is it…
baf
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This is a variation of the colored socks in a drawer problem.

Suppose that instead of having one drawer, you have two drawers. Each drawer has some socks that are white and some that are black. Drawer 1 has w black socks and x white socks. Drawer 2 has y black socks and z white socks. w+x=y+z. If you take…
mark
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What is the probability that 5 randomly chosen cards in a deck add up to 40 or greater?

I have made a probability game, where you have to pull out any 5 cards without looking (from a deck of 52 cards), and if all five cards add up to 40 or more, they player pulling the 5 cards from the deck wins. What is the probability of winning the…
Aiden Sherry
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Moment generating function of two independent variables

The moment generating functions of two independent variables $X$ and $Y$ are $M_X(t)=\exp(2e^t-2)$ and $M_Y(t)=\left(\frac34e^t+\frac14\right)^{10}$. What are (a) $P(X+Y=2)$; (b) $P(XY=0)$; (c) $E[XY]$? For (a), I did it in two ways that…
jakuva
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What are the chances that 5 people are all born on the same day#?

Assuming 30-day months, given 10 people in a room. What are the chances that 5 or more people are all born on the same day#? (i.e., 5 born on the 28th, or 5 born on the 6th, etc) (EDIT: changed from chances of 5 to chances of 5 or more) I have…
joeslice
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