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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Probability - Couples randomly sitting at a table, calculate the probability that they are together

I'm currently practicing for my first actuarial exam and came across this problem. The posted solution doesn't make sense to me, and even if I'm right I don't know the correct way to do it. The problem: 13 married couples are seated randomly at a…
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Probability of passing this multiple choice exam

A multiple choice exam has 175 questions. Each question has 4 possible answers. Only 1 answer out of the 4 possible answers is correct. The pass rate for the exam is 70% (123 questions must be answered correctly). We know for a fact that 100…
Kendra
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What is the probability of being selected?

I don't know if I have enough data to calculate (or even estimate) this because I don't understand statistics, distributions, etc. 550 people took a test to try to gain entry to a school. There were 2 tests: one in English and one in math. The…
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an urn contains two green, three yellow and five red balls.

An urn contains two green, three yellow and five red balls. We draw one ball at random and put it aside. then we draw another ball until there are no more balls. Find the probability of drawing at first the two green balls, then the three yellow…
Cash Vai
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Intuition for Prokhorov metric and metrization of weak convergence

According to Billingsley, let $P$ and $Q$ be two probability measures. Then the Prokhorov metric $\pi (P,Q)$ is the infimum of those positive $ \epsilon $ for which the two inequalities $PA \le QA^{\epsilon}+ \epsilon$ and $QA \le PA^{\epsilon}+…
webster
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Coin tossing question

Adam, Bertrand, and Carissa toss a coin in sequence until one person wins by tossing the first head. If the coin is fair, find the probability that Adam wins. Can somebody tell me if I'm on the right track? Adam can win on the first round if he…
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What's the distribution of gaussian squared with mean $\mu$ and variance $\sigma^2$?

Based on my understanding, Chi square distribution and noncentral Chi-squared distribution are used for special Gaussian distribution. However, when the Gaussian is not standard and with no unit variance, how could I calculate the distribution of…
linda
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Prove an inequality similar to Jensen's inequality

Prove that $$\mathbb{E}(\sqrt{X})\leq\sqrt{\mathbb{E}Y}$$ where random variables $X,Y>0$ and $\mathbb{E}\left[\frac{X}{Y}\right]\leq1.$ My attempt: This looks very much like Jensen's inequality. According to Jensen,…
lovelesswang
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Strategies to guess choices for multiple choice questions

Multiple choice questions (MCQs) are common in examinations over here in Singapore. A set of, say, $40$ questions are given to students, and each is accompanied with a list of $4$ choices of answer, $A, B, C$ or $D$. Suppose a student did not study…
Yiyuan Lee
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Problem about the sum of independent exponential variable

Let $X_1,\ldots,X_{n}$ be independent exponential variables with mean 1, and let $S_k = X_1+\cdots+ X_k$, it is not hard to get $\mathbb{E}(S_k)=k$. Let random variable $Y_k=|S_k-k|$, My first question is: what is the probability of $Y>t$ for some…
Fan Zhang
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What is the probability that both roots of the equation $Ax^2 + Bx + C = 0$ are real?

Given this problem as part of prep for a test. We've done the same problem without A being a random variable, but I am completely stumped as to how to accomplish this one with three r.v.s I know the joint is $1/288$ and that $B^2>4AC$ but cannot…
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Probability of winning a baseball game

Ok so here is my question. If the Tigers (team A) win 66% of the games they play on Tuesdays and the Sharks (team B) win 55% of the games they play on Tuesdays. Now when they play each other on a Tuesday what are the true chances of each team…
Beto
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Probability that a family with $n$ children has exactly $k$ boys

Let the probability $p_n$ that a family has exactly $n$ children be $\alpha p^n$ when $n\geq1$, and $$p_0=1-\alpha p(1+p+p^2+\cdots).$$ Suppose that all the sex distributions have the same probability. Show that for $k\geq1$ the probability that a…
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Which is the correct way to calculate the expected value of a shared lottery jackpot?

I want to calculate the expected value of a ticket in a lottery game which gives players a probability $p$ of winning a jackpot prize of $j$ dollars. The total number of tickets in play is $t$. If every winning ticket gets the full prize amount, the…
cristoper
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A and B play until one has 2 more points than the other...

Question A and B play until one has 2 more points than the other. Assuming that each point is independently won by A with probability p, what is the probability they will play a total of 2n points? What is the probability that A will win? My attempt…
JoeyAndres
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