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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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Probability / Discrete Random Variables

(a) Let $X$ and $Y$ be two independent discrete random variables. Derive a formula for expressing the distribution of the sum $S = X + Y$ in terms of the distributions of $X$ and of $Y$. (b) Use your formula in part (a) to compute the distribution…
Herman Chong
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Probability of two independent standard normal random variables

Suppose we have $X,Y$, two independent standard normal random variables. How can we calculate $P(|\min(X,Y)|<1)$. I am still learning multivariables probability, and I also realize there are a lot of nice properties of two standard normal r.vs but…
geraldgreen
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Approximate the probability

An immortal snail is at one end of a perfect rubber band with a length of 1km. Every day, it travels 10cm in a random direction, forwards or backwards on the rubber band. Every night, the rubber band gets stretched uniformly by 1km. As an example,…
Murtuza Vadharia
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Find the expected value from a point to three edges of a right triangle.

Given a right triangle with a, b, c are the lengths of three edges. Here $a^2=b^2+c^2$. A point is randomly chosen inside the right triangle. Find the expected value of the sum of the distances from the point to three edges.
Nguyen
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Expected value of number of tosses until we get $k$ tails and $k$ heads

Let $k$ be a fixed positive number. We toss a normal coin until we get at least $k$ heads and at least $k$ tails (not necessarily consecutively). Let $X$ be number of needed tosses. Find distribution of $X$ and its expected value. So this is my…
Anne
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Probability question related to coin tosses

In an exam I gave recently, the following question was asked: A fair coin is tossed $10$ times and the outcomes are listed. let $H_i$ be the event that the $i^{th}$ outcome is a head and $A_m$ be the event that the list contains exactly m heads,…
Shashank
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One container contains 6 red and 4 white balls, while a second container contains 7 red and 3 white balls

One container contains 6 red and 4 white balls, while a second container contains 7 red and 3 white balls. A ball is chosen at random from the first container and placed in the second. Then a ball is chosen at random from the second container and…
alex
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Find the probability of n different people having the same birthday month

Find the probability of n different people having the same birthday month. Is the following the right way to do: Choose any one of the n people. Then the rest must have the same birthday month as the chosen one. So the probability is: $n…
user10024395
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How many correct answers does it take to fill the Trivial Pursuit receptacle?

My friends and I likes to play Trivial Pursuit without using the board. We play it like this: Throw a die to determine what color you get to answer. Ask a question, if the answer is correct you get a point. If enough points are awarded you win We…
Archimedes
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Conditional Probabilities

I am faced with this question: $10$% of all email you receive is spam. Your spam filter is $90$% reliable, that is, $90$% of the mails it marks as spam are indeed spam and $90$% of spam mails are correctly labelled as spam. If you see a mail marked…
pranavashok
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Convergence in distribution of product of two sequences of random variables

For random variables $\{X_n\}$, $\{Y_n\}$ that converge in distribution to X and Y, what would it mean if $\{(X_n,Y_n)\}$ converges in distribution to (X,Y)?
DumbQuestion
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Distribution function of an exponential random variable

I am trying to answer the question $F(x)$ is distribution with $F(0)=0$ and $F(x)<1$ for some $x>0$. Show $F(x)$ is the distribution function of an exponential random variable iff $$F(x+y)-F(y)=F(x)\left(1-F(y)\right).$$ I started with the CDF of…
user130614
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How to calculate the distribution within a series

The probability of event $A$ happening is $50.7\%$. The probability of event $B$ happening is $49.3\%$. What is the probability that in a series of $100$ trials, there will be at least one point where more event $B$'s will have happened than event…
Tom Ware
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Probability that random byte array is a valid UTF-8 string?

What is the probability that $n$-byte random byte array is a valid UTF-8 string? It doesn't care if it's NFC or NFD.
Izumi Kawashima
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probability: when to multiply when to add?

The "classic" high school probability exercises most of the time ends up in a tree of possibilities that deals with all the scenarios (combinations?) that are possible for a given scenario: be it coin tosses, balls in a jar, anagrams, etc. But there…
Draconar
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