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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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Find probability that Rahul examines fewer policies than toby

$$ \underline{ \bf Attempt} $$ Let $X$ and $Y$ be the policies examined by rahul and toby, respectively. By the manner this problem is phrased we have two Bernoulli r.v. For instance, $X$ has probability success of $0.1$, thus $$ p_X(x) = {n…
James
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Probability two withdrawn balls are the same color

Suppose we have $n$ white and $m$ black balls in a urn. First, randomly withdraw two balls, what is the probability (Call it $P_1$) that they are the same color? Now, suppose a ball is randomly withdrawn and then replaced before second one is drawn,…
James
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How to make repeat winners unlikely in B.I.N.G.O.

My three-year-old son loves BINGO (U.S. version). This morning I took him to observe "senior BINGO" at a local fast food joint, and something interesting (though not surprising) happened: After a certain amount of numbers had been announced, senior…
The Chaz 2.0
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Probability of two integers' square sum divisible by $10$

Given two random integers $a$, $b$ calculate probability of $a^2$ + $b^2$ is divisible by $10$. I've tried to simulate this process and got a result about $0.18$ (maybe incorrect), but have no idea why.
halfelf
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Scaling of random variables

Note: I will use $\mathbb{P}\{X \in dx\}$ to denote $f(x)dx$ where $f(x)$ is the pdf of $X$. While doing some homework, I came across a fault in my intuition. I was scaling a standard normally distributed random variable $Z$. Edit: I was missing the…
angryavian
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CDF related to sampling with replacement

Consider a random process where integers are sampled uniformly with replacement from $\{1...n\}$. Let $X$ be a random variable that represents the number of samples until either a duplicate is found or both the values $1$ and $2$ have been found. …
user54551
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Why is the probability of picking an odd number from the set of natural numbers not $\frac{1}{2}$?

Why is the probability of picking an odd number from the set of natural numbers not $\dfrac{1}{2}$? Could anyone explain it to me in simple terms? I am only curious about the reason why and that's the reason why I asked for a "simple" explanation. I…
mrnobody
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An example of three probability events with certain property

I am trying to find three events $A,B,C$ with the following properties \begin{gather} P(A|B)>P(A),\\ P(A|C)>P(A),\\ P(A|B\cup C)
lkjhgfdsa
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Probability distribution for finding two values in stages

Fix two arbitrary distinct values from $\{1,\dots,n\}$. Say for concreteness we choose the values $1$ and $2$. We sample uniformly with replacement from $\{1,\dots,n\}$ in a number of stages. Each stage runs until we either sample the same element…
Whitehead
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How to divide $n$ people into two groups to maximize the probability of finding a lost boy

A small boy is lost coming down Mount Washington. The leader of the search team estimates that there is a probability $p$ that he came down on the east side and a probability $1 − p$ that he came down on the west side. He has $n$ people in his…
Max
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Intuitive explanations for Gaussian distribution function and mahalanobis distance

I was wondering If anyone could give intuitive explanations for the multivariate Gaussian distribution function and mahalanobis distance? My professor didn't explain these in probability class, they were only defined... Where did the formula come…
jjepsuomi
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Almost sure convergence for a sequence of random variables

I have read in some book that in case of almost sure convergence of a sequence of random variable it possible that $|X_{n}(\omega) - X(\omega)|$ can be extremely large for $\omega$ in a small probability set. How is that possible ? Here the sequence…
user21982
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Having event with probability $p$, how can I get an event with probability $\sqrt{p}$?

I'd like a design a circuit that, given a random bit with probability $p$ to be zero, it outputs a random bit with probability $\sqrt{p}$ to be zero. Actually, I am rather looking for $\sqrt{p(1-p)}$, in case it makes things easier. Let's assume…
Oersted
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Probability of all 3 cards drawn being the same number

Consider a scenario where Ace is considered as 1 (a number card) and the face cards (King, Queen, Jack) are not number cards. We have to find the probability of 3 cards drawn consecutively (without replacement) being the same number. My friend…
Siddharth Venu
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If I am 80% sure, is there an 80% chance that I'm right?

A friend of mine said this, and I couldn't argue why I thought it was wrong. Obviously, in some circumstances it is valid, say if you flip a coin, and I say I'm 50% sure it lands on heads. In a discussion about whether sending a "dick pic" was…
Chris Wohlert
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