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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A probability question that I failed to answer in a job interview

There are $N$ different sized targets, numbered $1, 2,\dots, N$. A blindfolded shooter shoots towards random directions. Because target sizes are different, the hit probabilities of each target are different, say $p_1, p_2,\dots ,p_N$. A bullet…
AYang
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When you randomly shuffle a deck of cards, what is the probability that it is a unique permutation never before configured?

I just came back from a class on Probability in Game Theory, and was musing over something in my head. Assuming, for the sake of the question: Playing cards in their current state have been around for approximately eight centuries A deck of playing…
Justin L.
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A probabilistic game with balls and urns

We have $N$ urns forming a circle and $M
leonbloy
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What is the expected number of steps in the following process?

We have $n$ boxes. And initially there are $x_1, x_2, x_3, \ldots, x_n$ marbles in each box. We randomly (with equal probabilities) select one of the boxes. We take one marble from it and we put it into another (different from the origin) box chosen…
Roah
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Expected value of the number of flips until the first head

Suppose we flip a coin until we see a head. What is the expected value of the number of flips we will take? I am pretty new to expected value, so I tried to evaluate it by multiplying the probability of each scenario with the number of flips it…
hyperdo
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% of % - Please Help Me Prove My Friend Wrong

Here is the situation: My friend and I are at an impasse. I believe I'm correct, but he's so damn stubborn he won't believe me. Also, I'm not the most articulate at explaining things. Hopefully some of you guys can help me explain this to him in…
Trynn
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Can you pick a random natural number? And a random real number?

Is it possible to pick a random natural number? How about a random real number? Is the axiom of choice involved in this?
Martijn
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What is the distribution of a random variable that is the product of two normal random variables?

What is the distribution of a random variable that is the product of two normal random variables? Let $X\sim N(\mu_1,\sigma_1), Y\sim N(\mu_2,\sigma_2)$ and $Z=XY$ That is, what is its probability density function, its expected value, and its…
Clara
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Average length of the longest segment

This post is related to a previous SE post If a 1 meter rope …. concerning average length of a smallest segment. A rope of 1m is divided into three pieces by two random points. Find the average length of the largest segment. My answer is 11/18. …
TCL
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What is the difference between multinomial and categorical distribution?

Both seem to result in one of k different separated outcomes, and Wikipedia says these are often conflated. Despite reading the explanation of the difference on the article about multinomial distribution, I still have trouble understanding what the…
user93603
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Independent odds, am I (+ friend) seeing this wrong or is there a mistake in the practice exam?

I found this exercise in a practice exam: Any student has a 90% chance of entering a University. Two students are applying. Assuming each student’s results are independent, what is the probability that at least one of them will be successful…
Cdl
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What are Belgium's chances on getting a medal at the 400m finals, given that they have 2 of the 8 athletes?

This is a question my wife and I pondered over at the breakfast table this morning: Belgium has two athletes in the finals of the 400m at the World Championship athletics this year. What are Belgium's chances of getting a medal, assuming every…
Peter
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coin toss question

Two players A and B each has a fair coin and they start to toss simultaneously (counted as one round). They toss in $n$ ($\ge 1$) rounds and stop because they have accumulated the same number of heads (could be 0, the case that both of them did not…
Qiang Li
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Probability distribution function that does not have a density function

What is an example of the probability distribution function that does not have a density function?
user12586
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I can't understand how probability makes sense

I have a lot of questions regarding probability. Please forgive me if I have made mistakes. I actually tossed a coin 200 times. 54% of the time it landed on heads and 46% it landed on tails. What is the reason that there is a fair chance of the…