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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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Two player pool, probability of winning

I have what seems like a simple question, but it's been a while since I've done any P/S. So i come to SE for help! Two player pool/billiards: P1 has probability p of sinking a ball on any shot and has N balls remaining, while P2 has prob q and M…
im so confused
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3 cards are dealt from a well shuffled deck.

1.Find the chance that none of the cards are hearts. The answer is $\frac{39}{52}$ $\cdot$ $\frac{38}{51}$ $\cdot$ $\frac{37}{50}$ However, why can't we use complement rule here: 1- p(chance that all the cards are hearts)= 1- ($\frac{13}{52}$…
jasminvvian
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Six dice blank on five sides. How to roll as one?

I have six six-sided dice. Five of their faces are blank and identical. One face on each die contains the number 1,2,3,4,5, or 6. Suppose I roll them together, the output from this random event is an unordered set for example: {B,B,3,1,B,6} (blank…
futurebird
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Probability : Roll of Die

$\textsf{A}$ and $\textsf{B}$ are playing a game with $2$ standard dice. Both the dice are rolled together and the total is counted. $\textsf{A}$ says that a total of $2$ will be rolled first. $\textsf{B}$, whereas, says that two Consecutive…
S.Rana
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Probability of Barcelona playing Real Madrid in Champions League Quarterfinals

The $2018$ Champions League quarterfinal draw will take place on Friday, March $16^{th}, 2018$ and I wanted to know what is the likelihood that Barcelona will get paired up with Real Madrid? There are $8$ teams left in the pool so a total of $4$…
user8463863
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conditional expected value given the random variable is less than another random variable

Assume two independent random variables $X$ and $Y$ with p.d.f. $f(x)$ and $g(y)$. For simplicity, both $X$ and $Y$ are positive. How to find $E[X|X
Much Sal
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Voting score paradox

These is a voting system, where a user can place one of the three types of votes: $NEG, NEUT, POS$ Let's call a voting configuration (VC for short) total number of NEG, NEUT and POS votes left by the users. (E.g. $N_{neg} = 5, N_{neut} = 10,…
Denis Kulagin
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1st Yr Probability: question about marginal and joint pdfs for $3$ uniform continuous independent random variables

Background I'm trying to improve my understanding of the relationship between marginal and joint pdfs for calculating specific probabilities. The Problem $X$, $Y$, $Z$ are independent and uniformly distributed $(0,1)$. What is $P(X>YZ)$? My…
HJ_beginner
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Probability Problem based on the a set of numbers. Determine if the number is divisible by three

Three distinct numbers are selected at random from the set $\{1,2,3,4,5,6\}$. What is the probability that their product is divisible by $3$? I think that since because $3$ and $6$ are the only numbers that divide into three with an integer…
Led Nowmann
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probability that subsets are successively contained

The set A has $n$ elements, and so has $2^n$ subsets. The subsets are placed into an urn, and $m$ subsets $B_1, \dots, B_m$ are drawn in order at random with replacement from the urn. (Each subset has probability $\frac{1}{2^n}$.) What is the…
tostito
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What are the most fundamental applications of probability theory outside pure math?

What are the most important / fundamental / classical applications of probability theory outside of pure math? What were some of the original "home runs" of probability theory -- things that we could not do before, but which were very useful. Things…
eternalGoldenBraid
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Calculating $\mathbb{P}(A \mid B)$.

To confirm the formula for probabilities, given that an event has occured, I wonder if it is true that: $\mathbb{P}(A \mid B)=1-\mathbb{P}(A^{C} \mid B)$ where $\mathbb{P}(A)+\mathbb{P}(A^{C})=1$. $A$ and $B$ are events.
Lindberg
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In a hand of 13 cards, what is the probability that all cards have different values

I'm going to go through my thoughts, tell me if I'm right. There are $52\choose 13$ different hands with 13 cards. Each value has to appear once with 4 suits for each so there are $ 4^{13}$ different hands with each number once. So i conclude that…
Malcolm Hall
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A very basic probability question

Suppose that I have $n$ objects and I make $m$ choices (with repetitions) out of the objects. Then what is the probability that no two of my choices are the same?
henry
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Binomial Distribution and Normal Distribution

Today at school we discussed probability distributions and as usual my mind wandered off and I started thinking: Normally when we have a die, you can make a binomial distribution. So I thought, if you have a die with, instead of 6 sides, an infinite…
JohnPhteven
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