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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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Deal 4 cards from a deck. What is the probability that we get one card from each suit?

My simple easy homework question. Just needed some double check :D Deal 4 cards from a deck of 52 cards. What is the probability that we get one card from each suit? My answer First Draw: We can get any card, and the card's suit will be done.…
Yellow Skies
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Flip a fair coin until three consecutive heads or tails appear

What is the expected number of flips until three consecutive heads or tails appear?
LittleSweet
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Roll a dice infinite times BUT pay $1 to play - strategy?

I am stuck with a question related to the optimal strategy of rolling a dice. Its an extension of the problem "Roll a dice and take either the amount on the dice or re-roll (a maximum of twice)". Heres the link to the basic version and solution: The…
Math525
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What's the probability that Abe will win the dice game?

Abe and Bill are playing a game. A die is rolled each turn. If the die lands 1 or 2, then Abe wins. If the die lands 3, 4, or 5, then Bill wins. If the die lands 6, another turn occurs. What's the probability that Abe will win the game? I think…
David Faux
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Calculating probability of winning best-of-7-games tournament. Why is my method wrong?

The question is as follows: A and B participate in a tournament of "best of 7 games". It is equally likely that either A wins the game or B wins the game, or the game ends in a draw. What is the probability that A wins the tournament? So I tried…
FreezingFire
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What is the difference between conditional and posterior probability?

I'm having having understanding the difference between conditional and posterior probability. Conditional probability: ...a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has…
tim_xyz
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Probability that a man will hit the target

The question is A man can hit a target once in $4$ shots. If he fires 4 shots in succession, what is the probability that he will hit his target? Here is how I am solving it: Since the probability of man hitting the target is $\frac{1}{4}$ so…
MistyD
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The probability of one Gaussian larger than another.

For two Gaussian-distributed variables, $ Pr(X=x) = \frac{1}{\sqrt{2\pi}\sigma_0}e^{-\frac{(x-x_0)^2}{2\sigma_0^2}}$ and $ Pr(Y=y) = \frac{1}{\sqrt{2\pi}\sigma_1}e^{-\frac{(x-x_1)^2}{2\sigma_1^2}}$. What is probability of the case X > Y?
Strin
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A probability game

Motivation: A friend asked me this question. The Problem: Suppose you start off with a dollar. You flip a fair coin, if it lands on heads you win $50$ cents otherwise you lose $50$ cents. If after $n$ flips you have a nonzero amount of money, you…
user899
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CDF of absolute value of difference in random variables

Let $X$ and $Y$ be independent random variables, uniformly distributed in the interval $[0,1]$. Find the CDF and the PDF of $|X - Y|$? Attempt Let $Z = |X - Y|$, so for $z \geq 0$, the CDF $F_{Z}(z) = \mathbf{P}(Z \leq z) = \mathbf{P}(|X - Y| \leq…
buzaku
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Is it unlikely to get the same number of heads/tails?

A question in probability by a non-mathematician: A fair coin is tossed $2N$ times. Is it unlikely that we get exactly $N$ heads and $N$ tails? From one side, this must be the most likely result! But intuitively, if someone reports to me that they…
Tom Y
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Variance formula in terms of the CDF for a continuous nonnegative random variable.

Is there a formula for the variance of a (continuous, non-negative) random variable in terms of its CDF? The only place I saw such formula was is Wikipedia's page for the Variance (https://en.wikipedia.org/wiki/Variance). Unfortunately, I was not…
Felipe Schoemer Jardim
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Curious about a made-up paradox

I have thought up a paradox, that may already exist, but I do not know what it's called. It's bothering me though, so any help regarding solving it or proving it impossible would be appreciated. In this paradox, you have a gambler. The gambler is…
Dmytro
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How to win at roulette?

I know that the answer to my attention-grabbing question is : "You can't win at roulette, it's a negative Expected Value game". Yes, you're right, long term speaking. Let's imagine a medium-short term situation (just an after-dinner at the casinò)…
KingBOB
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Probability: the average times to make all the balls the same color

Suppose there are n balls with different colors with each other in a bag. In one loop, One take two balls in sequence out of the bag and replace them with two balls with the same color of the first ball. Q: how many loops does it take to make all…
Peter
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