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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 .

105859 questions
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Picking first or picking last

We've had quite a debate in our family regarding this one. Five guys want to share a house with five bedrooms. Room 5 is smaller than the rest and no one wants to pick it. To decide which room they get, they put five pieces of paper in a bag,…
Mike Lapenna
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Maximum of $k$ binomial random variables?

Imagine you have $k$ random variables $X_1,...,X_k$ drawn i.i.d. from a binomial distribution $B(n,1/2)$. For any $\epsilon > 0$, the probability that the maximum of these $k$ draws is above $(1-\epsilon) n$ $$ \Pr[\max_i X_i > (1-\epsilon) n] =…
Asterix
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Probability of truth in a chain of statements

Three individuals $A$,$B$ and $C$ tell the truth with probability $1/3$. (A) $C$ makes a statement and $A$ claims that it is true. What is the probability that the statement is true. (B) $C$ makes a statement and $A$ tells you that $B$ claims the…
Miz
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Expected length of runs in a binary string

Question This is a math of the Introduction to Probability Models (11th edition) written by Sheldon M Ross. Runs of 0s or 1s follow a geometric distribution. The solution I found in the solution manual: Answer Here conditioning has been applied on…
Preetom Saha Arko
  • 175
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Lower bound on $P(X>\lambda)$ where $X$ is Gaussian.

Suppose X is a 0 mean Gaussian random variable with variance 1. I'm trying to find a lower bound on $P(X>\lambda)$. Specifically I'd like to derive a lower bound of the form $c e^{-C\lambda^2}$ for positive constants $c,C$. I know there exists…
Mykie
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Probability puzzle about crossing lights – what is wrong with my reasoning?

Calvin has to cross several signals when he walks from his home to school. Each of these signals operate independently. They alternate every 80 seconds between green light and red light.At each signal, there is a counter display that tells…
user126540
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Probability of area being greater than 0.5 with random lines

Take the square $[0,1]^2$ we take $n$ random lines through the square. You can choose random lines by choosing a point on one of the sides of the squares and randomly choosing a different point on any of the other three sides and then drawing a line…
user402817
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Does CLT fail in this case?

We have mutually independent random variables $X_n$ with $P(X_n = 2^n) = P(X_n = -2^n) = \frac12$. Of course their means $\mu_n = 0$ and variances $\sigma_n^2 = 4^k$. Let $S_n = \sum_1^n X_k$. Clearly the mean $m_n=E(S_n) = 0$ and variance $s_n^2 =…
nullUser
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Probability distribution and mathematical expectation in a process of handling tasks

Assume there is a task pool which has $m$ unprocessed tasks. There are $n$ processors to process the tasks. The rules of processing tasks are: The processors pick up tasks in the task pool randomly. At each round, all the processors will get a…
s9527
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finding the optimal strategy

You have a deck of 32 playing cards. Somebody draws one card after another and shows them to you. At any point of time you may bet that the next card is black. If it is indeed black you earn $10, otherwise nothing. If you don't do anything you earn…
QuasiK
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Probability of rolling 3 and 4 in a row with 4 6-sided dice

So I was playing a game and was wondering what the probability was to roll numbers in a row. Four fair six-sided dice are rolled. What is the probability that three of the numbers will be in a row. Also, that all 4 of them will be in a row. I've…
Aaron
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determine the probability of each value multiple rolls of dice. stop once same number shown N times

Trying help my daughter with a problem. The problem: Two dice. Each numbered 1-6. Both dice are rolled at the same time to get one of 11 values in the range 2-12. The 11 values have a different probability of occurring: Number 2 has 1/36 probability…
camios
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Probability of choosing bat

I got the option A and B by manually checking but after that got stuck .
Koolman
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Expected winnings on a coin flip game

A game involves flipping a coin until the first head appears and winning $2^n$ dollars if the first head appears on the $\mathrm{n^{th}}$ coin flip. We want to determine the expected winnings for this game. Based on my understanding on the…
Rob
  • 511
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Why does bayes theorem frequently have sum in denominator?

I frequently see Bayes Theorem phrased in two different ways. Simple Bayes Theorem: $$P(X|Y) = \frac{P(X)P(Y|X)}{P(Y)}$$ Complex Bayes Theorem: Let $X_1, \dots, X_k$ be a partition of the sample space. $$P(X_i|Y) = \frac{P(X_i)P(Y|X_i)}{\sum_{j =…
zrbecker
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