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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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Calculating the probability of seeing a shooting star within half an hour if we know it for one hour

The probability to see a falling star in the sky over the course of one hour is 0.64. What is the probability to see it over the course of half an hour?
Maxime Vernier
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Seating of $n$ people with tickets into $n+k$ chairs with 1st person taking a random seat

"$n$ music lovers have reserved seats in a theater containing a total of $n+k$ seats ($k$ seats are unassigned). The first person who enters the theater, however, lost his seat assignment and chooses a seat at random. Subsequently, people enter the…
ithisa
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expected area of a triangle determined by randomly placed points

Three points are placed at independently and at random in a unit square. What is the expected value of the area of the triangle formed by the three points?
yrudoy
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If n people randomly pick one hat out of $n$ hats, why is the probability of a match $1/n$? What about order of previous hats?

For a standard matching problem There are $n$ people with hats at a party. Each person randomly grabs a hat. A match occurs if a person gets his own hat. Define the number of matches $N$ as $$ N=\sum_{k=1}^n X_k, $$ where $X_k$ is the…
user14108
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Probability of drawing all 4 balls

A Greek urn contains a red, blue, yellow, and orange ball. A ball is drawn from the urn at random and then replaced. If one does this $4$ times, what is the probability that all $4$ colors were selected? I approached this questions by doing…
minatozaki
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Probability that three independent uniform $(0,1)$ random variables can form a triangle

I am preparing for a probability exam and while practicing stuck on this question. Do not even know how to begin. Let $X_1$, $X_2$, $X_3$ be independent uniform $(0,1)$ random variables. What is the probability that we can form a triangle with three…
user669083
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Expected value of the max of $2$ dice

What is the expected value of the max of two dice? I just wonder if there's a better way to get the answer to this question than listing out all possible outcomes and determining the expected value from there as this is actually an interview…
Jojo
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Should I join a group, or stay an individual?

I have just taken part in a draw and it has left me wondering whether I made the right decision to enter the draw as an individual or whether I should have entered as a group, and if so, what size group would have been optimal. For this draw my…
Mark Booth
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What is the probability of getting yahtzee?

What is the probability of getting a yahtzee using $N$ dice with $X$ sides in $Y$ throws in a single round? Which side of the dice appears on the yahtzee with doesn't matter (i.e. it doesn't matter if I throw ones, or twos, etc.). I also assume…
runaros
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What is the probability that $XYZ$ is divisible by $5$?

A solution of $X + Y + Z = 20$ in non-negative integers is chosen at random. What is the probability that $XYZ$ is divisible by $5$? Edit: This happens to be an exam question. So I can't use calculators or computers and have to get the answer in…
hollow7
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Toss a fair coin a number of times.

Toss a fair coin, number of times. You always bet on heads and gain one dollar if it is a head and lose one dollar if it is a tail. You stop whenever you gain 3 dollars or you lose 2 dollars. Then which of the following is the correct one? you end…
user109403
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Compute the expectation of steps making $n$ different balls the same

Suppose that we are given $n$ balls of different colors. Each time we pick up two balls randomly and change the color of the second ball to that of the first, then we put them back. The question is what is the expectation of steps when these balls…
Ma Ming
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If three dice are rolled, what is the probability that all three are the same number?

The dice are fair. You have a $1\over6$ chance of getting the first number. A $1\over6$ chance of the second and so on. Is it just $({1\over6})^3$ (1/216) or is that not accounting for the second and third roll properly?
switz
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Intuition for partial averaging eqution

I just learnt about the condition expectation and as is known, the definition is as follows: My question is for the second property (partial averaging property), what kind of intuition does it express? How can I understand in a more perceptual way.…
Brain Zhang
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Probability that last child is a boy

Johnny has 4 children. It is known that he has more daughters than sons. Find the probability that the last child is a boy. I let A be the event that the last child is a boy, P(A) = $\frac{1}{2}$. and B be the event that he as more daughters than…
user9234
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