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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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What's the probability of choosing two numbers from $[0,1]$ and having the difference at least one half?

We have the unit interval $[0,1]$ and we want to find the probability of picking two random numbers $a,b$ from that interval with $|a-b|>0.5$. Must I investigate $[0,1]×[0,1]$? I don't have the faintest idea of how to solve this. The problem is that…
Konstantinos Nikoloutsos
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What is the expected length of the largest run of heads if we make 1,000 flips?

Is there a way to calculate on average, the maximum amount of times we can expect a coin to land heads during 1,000 flips? So the answer (and formula if one exists) I am looking for would be something like: during 1,000 flips we can expect a maximum…
Juan Velez
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Probability, conditional on a zero probability event

Is there a way to resolve probability of an event, given another event that never happens? Mathematically speaking the problem is: Given that $P(B) = 0$, $$P(A|B)=\frac{P(A \cap B)}{P(B)} = \frac{0}{0}$$ Is this probability vacuously $0$ of $1$? Can…
Phonon
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How to calculate the expectation of $XY$?

Suppose I am given the joint pdf of $X$, $Y$, and I am asked to find the $\operatorname{cov}(X,Y)$. I know that $\operatorname{cov}(X,Y)=E(XY)-E(X)E(Y)$ and I know how to find $E(X)$ and $E(Y)$. My questions are: What is the definition of $E(XY)$?…
breezeintopl
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Obtaining irrational probabilities from fair coins?

Suppose I have access to a fair coin. Is it possible to come up with a procedure that (1) returns TRUE with irrational probability (say $1/\sqrt{2}$) and FALSE otherwise, and (2) terminates in a finite amount of time? I would think not, because at…
Elliott
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What are my chances in a Most Excellent Adventure?

Most Excellent Adventure is a home brew roleplaying game system based on the Bill & Ted Films, plays gnarly air guitar riff. In this game system, when you draw from your dice pool you need to connect the results as a phone number on your phone…
AncientSwordRage
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Probability problem: cars on the road

I heard this problem, so I might be missing pieces. Imagine there are two cities separated by a very long road. The road has only one lane, so cars cannot overtake each other. $N$ cars are released from one of the cities, the cars travel at constant…
Ivan
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3 other extensions of the Secretary Problem

In the classical secretary problem (also known as Marriage, Sultan's Dowry, Gogol problems), There are $n$ candidates ordered from the best to the worst (no ties). We know $n$. The candidates arrive sequentially in random order (uniform…
Jean-Pierre
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Random Dental Floss Odds

Awhile back I bought 2 identical rolls of dental floss, each with 50 uses, and picked them randomly. Tonight, the one I picked hit the 50 use mark. What is the expected number of uses in the remaining roll? With a 100000 case brute force, I get…
Ed Pegg
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Stars in the universe - probability of mutual nearest neighbors

If the stars are distributed randomly within the universe, what is the probability for a star to be the nearest neighbor of a star that is its nearest neighbor? What if the number of spatial dimensions is higher than 3 or even grows without limit?…
Johannes
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What is the expected value of the largest of the three dice rolls?

You toss a fair die three times. What is the expected value of the largest of the three outcomes? My approach is the following: calculate the probability of outcome when $\max=6$, which is $$P(\text{at least one $6$ of the three rolls}) = 1 -…
Jovoszhou
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how to find the expected number of boxes with no balls

If you have 10 balls and 5 boxes what is the expected number of boxes with no balls. The probability that each ball goes independently into box $i$ is $p_i$ with the $\sum_{i=1}^5 p_i =1$. Also, what is the expected number of boxes that have exactly…
lord12
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Difference between a joint probability and the probability of an intersection

Is the joint probability $p(X=x,Y=y)$ equivalent to $p(X=x \cap Y=y )$? If it is, why do we use two different notations?
usual me
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Does the square of uniform distribution have density function?

$X\sim U[0,1]$ and $Y\sim U[-1,1]$ are two uniform-distributed R.V.'s. Are $X^2$ and $Y^2$ still uniform? Do they have explicit probability density funtion?
JFK
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another balls and bins question

I've seen many variations of this problem but I can't find a good, thorough explanation on how to solve it. I'm not just looking for a solution, but a step-by-step explanation on how to derive the solution. So the problem at hand is: You have m…
Hristo
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