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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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The average of $X_iX_j (i\neq j) $ goes to $\mathbb E(X)^2$ in probability

Suppose $(X_n)_n\geq 1$ are i.i.d. $\mathbb E(X)=\mu$, $\sigma^2= \operatorname{Var}(X)<\infty$. I want to show $$\frac 1 {n(n-1)} \sum_{1\,\leq\, i,j\,\leq\, n,\,\, i\,\neq\, j} X_iX_j\to \mu^2$$ in probability. Here is what I tried. Applying…
Eddie
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probabilitiy: roll die $12$ times get each side twice

this is my 3rd question today ^^ Thanks a lot for any help :-) I need to calculate how probable it is if i roll a die 12 rounds and i get each side twice. Idea: Because every side needs to be present twice and we roll the die 12 times: $$ \left (…
hukachaka
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Two probabilities of the same thing

Consider this minesweeper situation. The 3 I've circled tells us that there is a mine in one of A, B and C. So, this means the probability that the mine is in A is $\frac{1}{3}$. And the 4 I've circled (and the 2 below it) tells that there is a mine…
user402662
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Expected Payoff for Dice Game Where Six = No Payoff

In a dice game where a player's payoff is whatever the die is rolled, each player can roll how many times they want. Each payoff gets added cumulatively (e.g. roll 5 and 5, then payoff = 10). The catch is that if the user rolled a six at any point…
rawr rang
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Answer verification for Binomial Distribution problem

Question: You buy a certain type of lottery ticket once a week for 4 weeks. What's the probability you win a cash prize exactly twice? My attempt: P(Success) = $1/4 $ P(Not Successful) =$ 3/4$ $$4 \ _nC^r \ 2 \times \bigg(\frac{1}{4}\bigg)^2…
obsolutemal
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Rolling die until number is greater than 100

Possible Duplicate: Probability of dice sum just greater than 100 A die is rolled several times and the number appearing is summed. We stop when this sum becomes greater than or equal to 100. What value of sum in the end is the most probable (out…
damned
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What is the probability that you win the second game given that you won the first if the outcomes of the two games are independent?

I’m working on a probability problem, but I’m having a hard time understanding the question exactly. The problem is: You are going to play two games of chess with an opponent you have never played against before. Your opponent is equally likely to…
t_hee
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Conditional probabilities and order of operation

I see terms of the form $P(A|B,C)$ a fair bit. Which of the following is true? $P(A|B,C)$ is the joint probability of $A|B$ and $C$ $P(A|B,C)$ is the probability of $A$ given both $B$ and $C$
oadams
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There is a phone number with $10$ digits. What's the probability that each digit occurs exactly once?

There is a phone number with $10$ digits. What's the probability that each digit occurs exactly once? This is a task of an old exam and I'm curious if my solution is correct. So we have a phone number made up of $10$ digits. Any number between…
cnmesr
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Probability of getting a white a ball after $4$ balls are drawn

A bag contain $6$ Red and $4$ White balls. $4$ balls are drawn one by one without replacement and were found to be at least $2$ white.What is the probability that next draw of a ball from this bag will give a white ball.? My try: As there were at…
Mathematics
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Probability of not finding a joker among 54 cards until the 54th draw?

I manage a "Joker Poker Raffle" for a veterans club in Shelton, WA. We start each round with 54 cards (4 suits @ 13 cards plus 1 mini Joker and 1 Jackpot Joker) sealed in identical envelopes. Each Saturday we sell tickets and then draw one ticket…
Brian Walsh
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Probability of winning tic tac toe game.

You and your friend like to play tic tac toe, but are not very good at it. On each turn, the player picks a random empty square to place their mark. The game ends when the first person gets three in a row, as usual. If you make the first move, what…
Soumee
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probabilities on multiple choice questions

I am setting a series of multiple choice questions. I have a range of option answers from 2 to 7. Some questions only have a single correct answer and others have more. I can tell the person taking the test what number are correct, or I can just…
russlater
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A probability problem involving two decks of cards

Here is the problem: Player A chooses 5 cards from a deck of cards. Player B also chooses 5 cards from ANOTHER deck of cards. Player B wins if his cards match at least 3 cards of player A. What is the probability that the number of cards of player…
Yuumi
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Intro Probability Question

Of $33$ people, $17$ like red, $14$ like green, and $11$ do not like either. What is the probability that a student likes red and green? What's the probability that exactly one of the following is true: the student likes red (call this event $A$) or…
soccerfan
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