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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 is the expected value of A?

The Happy Animals Kennel has 18 cages in a row. They allocate these cages at random to 6 dogs, 6 cats, and 6 pot-bellied pigs (with one animal per cage). All arrangements are equally likely. Let A be the number of times in the row of cages that two…
heyhuehei
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Expected value of sock pairs

Suppose that $N$ pairs of socks are put in a washing machine, with each sock having one mate. If the washing machine randomly eats socks, and at the end of the wash returns a random number $K$ of socks where $0 \leq K \leq 2N$, where each $K$ is…
stumped
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Probability and Expected Value of a guessing game

Let's say I think of a number between one and six. I will tell you to guess the number and tell you when it's wrong until you guess the correct number. What is the expected number of guesses before the correct number?
Seraphim
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Probability of being late

I would like help with correcting my solution for the following problem: Adam, Bob and Clare have made an appointment at 5 PM. Adam is never late. The probability that none of them is late is 0.4. If at least one of them is late, the probability…
michael
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correspondence between balls in compartments and integer vectors

I'm doing a self-review of probability and working through Ross' Introduction to Probability. The question is (Ross, ch2 number 51): suppose $n$ balls are randomly distributed into $N$ compartments. Find the probability that $m$ balls fall in the…
DavidT
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What is the probability of a number from 1-25 being an odd number or a factor of 20?

What is the probability of a number from 1-25 being an odd number or a factor of 20? Here's my working out: Odd numbers: 12/25 (1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25) Factors of 20: 6/25 (1, 2, 4, 5, 10, 20) Both: 2/25 (1, 5) P(odd number or…
Will
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Rolling a dice until we have $5$ and an even number.

We roll a dice, until we have both: a five and some even number. Let X be the expected number of rolls. Find expected value of X and Var(X). So I don't know how to begin. I think there should be something like $X= X_1 + X_2$ And then I would use…
Anne
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Rayleigh and Exponential distributions?

If $X$ is Rayleigh distributed random variable. What is the distribution of $|X|^2$? If $X$ is Exponential distributed random variable. What is the distribution of $|X|^2$?
x.y.z...
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Choosing something of $0$ probability

First of all, i am only a newbie and i am pretty sure that my thinking is faulty somewhere, so along the way as i explain things i will probably say something with an error and i hope you will help me find this error. This idea has been bogging me…
user151496
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Binomial Distribution: Finding the number of trials given probability and successess

Say we want to find the number of trials needed to be 90% sure that we will have at least two or more success, given the probability of a success is say, 50%. This question is easy when you want to find the number of trials for at least one…
Dom
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Help with the Probabilty of Rolling Two Ten-Sided Dice Multiple Times Until 100 is Reached

I need some help figuring out the probability of reaching or exceeding 100 based on a number of rolls of two, ten-sided dice. Here's the scenario. I am starting from zero. I am rolling two (fair) ten-sided dice, to generate a result between 2 and…
Discord
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Two people A and B throwing dice

A begins by throwing a dice until he gets $6$, then B does the same thing. What is the probability that A throws more times than B? I try to solve it, but I got 2 different answers: 1. We mark: $X=$How many times A throws, $Y$=How many times B…
CS1
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What's the probability of "at least" and "exactly" one event occurring?

If I know the probability of event $A$ occurring and I also know the probability of $B$ occurring, how can I calculate the probability of "at least one of them" occurring? I was thinking that this is $P(A \text{ or } B) = P(A) + P(B) - P(A \text{…
upabove
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Bound for probability of the intersection of a set of events

There are $N$ random variables $X_1,\dots X_N$ and $Pr(X_i=1)=p$ $\forall i\in N$. Can we upper bound the probability that all random variables are $1$, i.e., $Pr(X_i=1,\forall i\in N)$. Note that the random variables are not independent. Edit: How…
triomphe
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Almost sure convergence on an inductively defined random variable

Define a sequence of random variables inductively with $X_0=1$ and $X_{n+1}$ selected randomly and uniformly from $[0,X_n]$. Show $\dfrac{1}{n}\log X_n$ converges almost surely to a constant and evaluate the limit. A sequence of random variables…
chris
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