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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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Expected value of joint probability density functions

Quick question here. I'm trying to make sense of this problem... $$f(x_1,x_2) =\begin{cases} 8x_1x_2 & \text{for } 0 < x_1 < x_2 < 1\\ 0&\text{otherwise} \end{cases}$$ If $Y = X_1(X_2)^3$ , what is the expected value of $Y$? My thoughts: I'm not…
nicefella
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Expected value of a variable related to uniform r.v.

Let $X_i$ be i.i.d. uniform random variable on $[0,1]$. Let $N=\inf(n \colon \prod_{k=1}^n X_k < 10^{-3})$. What is $\mathbb{E}(N)$? I am trying to solve this but I am totally confused. How do I find an expected value for an infimum?
Delta9
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Number of possible pairs

I have a problem counting all the possible way of "pairing" 2 people in a group of N people (let's assume N is even). Example: The professor wants the students to work in pairs (groups of two). In how many ways the students could pairs ? I have…
azerty
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Chance of winning a raffle with a special rule

A person is hosting a raffle event. There are 1000 participants in the raffle. The raffle draw will produce one winner. The Special Rule The host is also 1 of 1000 participants, but he announces he will not claim the prize, so, if the host wins the…
maxi C
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Classic Hat Probability Problem

This is a textbook example and I am confused about the explanation. This question was asked by different people in stack-exchange already but I couldn't find the solution to my question. Here's the problem: At a party $n$ man take their hats. The…
Johnny Ton
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Possible draws in which exactly one player gets exactly one 8

The card deck has 30 cards in three different colors. Cards of each color are numbered 1 to 10. Each player draws 4 cards. The order in which cards are drawn to players' hands is not important. The question is in how many possible draws exist in…
HippoTerrific
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Probability each table leg was in each spot.

I have a fold up table at home with six legs and three areas. Each area takes 2 legs to keep the table up, but when stored three legs are positioned on the left and three on the right. Everytime I setup the table I randomly take the three legs on…
Hugo Delsing
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What is the probability that you get an increasing sequence of rolls if you roll it three times?

So, I know the answer to this question is: $$\frac{{6 \choose 3}}{6^{3}} = \frac{20}{216} = \frac{5}{54}$$ But I have no intuition. Why is the numerator ${6 \choose 3}$? Why is the numbers of ways to pick 3 from 6 equal to getting rolls in…
bananaboy
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Probability of winning games at tournament

I know it's a simple problem but apparently I am doing something wrong: The probability of winning every single game at a tournament is 0.4. There is only win and lose - no draw. Find the probability of winning exactly 2 games by playing at most…
Pradeep Suny
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Coin Betting Expectation

Suppose I have a biased coin with probability of heads p, and tails q=(1-p). It is then used in a game which lasts at most N tosses, and start with a stake of £1. Each time the coin is tails my money is doubled. The first time it comes down heads…
Richard123
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Coin flips and Dice rolls

A die is rolled 100 times, and the sum of the numbers that are rolled is recorded as X (for example, if a 6 is rolled every time, X = 600). A coin is tossed 600 times, and the number of heads is recorded as Y. Find P(X > Y). I know E[X] = 350 and…
Harry P
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Simple probability problems which hide important concepts

Together with a group of students we need to compose a course on probability theory having the form of a debate. In order to do that we need to decide on a probability concept simple enough so that it could be explained in 10-15 minutes to an…
Beni Bogosel
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Simple probability question, balls and bins

This is a simple question I came across in reviewing. I am wondering if I got the correct answer. The question is simple. You have $n$ balls and $m$ bins. Each ball has an equal probability of landing in any bin. I want to know what the…
user9470
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Seeking intuition on hat-check probability depending on parity of $n$

In (one version of) the hat-check problem, https://proofwiki.org/wiki/Hat-Check_Problem the question is to find the probability that for $n$ hat-checkers, nobody gets their own hat. If this is called $p_n,$ the solution is to obtain the $n$th…
coffeemath
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Probability is unique?

In many problems of probability the requirement is : Find the probability of (something). But a probability is a positive numeric function s.t: Axiom 1. $P(E)=1$ ,where $E$ is sample space. Axiom 2. Let $A_1,A_2,\ldots$ be a countable (possibly…
Ica Sandu
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