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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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Counting exercise

Three players a,b,c take turns in a game according to the following rules: At the start A and B play (so C does not play). The winner of the first trial plays against C and so on until one of the players wins two trials in a row. Possible…
zer0cube
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Probability of getting split pill from bottle?

I have a bottle of 100 pills. The daily dose is 1/2 pill, so if the first pill I extract is a whole pill, I split it and put 1/2 back. Just out of my own general curiosity, I'd like to model the probability of extracting a whole pill vs. a half…
jawns317
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How to work with random variables?

If $X$ and $Y$ are independent random variables described by standard normal distribution could you please explain how to formally evaluate probabilities of occurrences such as $X-Y>0$ (intuitively it's $0.5$ of course) or $X^2-Y^2>0$? Ultimately…
Pranasas
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Expected value of $|H-T|$ in $n$ coin flips

Let $H_n$ be the number of heads in $n$ coin flips. Let $T_n$ be the number of tails in $n$ coins flips. Is there a good way to calculate $E_n = E[|H-T|]$ that isn't brute force computation, i.e. directly evaluating $$E[|H-T|] = \frac{1}{2^n}…
Calvin Lin
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Round table seating logic question.

what is the probability of 5 people with different ages sitting in ascending or descending order at a round table. So, let me know if there's a better way to go about this problem. Let's have the people be named 1,2,3,4,5 They could…
Jwan622
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Finding out if a sequence of digits is a "numpad path"

I noticed that several of my old credit cards have verification codes which have an interesting property which I'll call "numpathable". A numpad is a graph that looks like this: 7 - 8 - 9 | | | 4 - 5 - 6 | | | 1 - 2 - 3 A number $n$ is a…
John Feminella
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Wimbledon's final

Tom and Jack are playing the final of Wimbledon and they are 6:6 at the last set. They play to the bitter end until one of them is ahead by two games. For Tom the probability to win the next games is $p$, and for Jack $1-p$. Every games is…
Francesco Totti
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Looking to optimise my Runescape grind (probability)

I know there's gaming stackexchange for gaming questions, but I believe this is purely maths related. I'll try to avoid using game jargon and keep it simple. I'm collecting keys in game, each key taking a fair bit of time to obtain. They open a…
user3767919
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Probability of getting exactly 2 heads in 3 coins tossed with order not important?

I have been thinking of this problem for the post 3-4 hours, I have come up with this problem it is not a home work exercise Let's say I have 3 coins and I toss them, Here order is not important so possible sample space should be 0 H, 1 H, 2 HH,…
Max
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A confusing question on probability

In a race, the probabilities of A and B winning the race are $\frac{1}{3}$ and $\frac{1}{6}$ respectively. Find the probability of neither of them winning the race. I solved the question in the following manner- Since A and B are running in…
Anurag Saha
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Please check my solution: probability that there is at least $2 \times 2$ square of just black squares

Suppose I had a $4\times4$ grid. Each square can be colored white, black, or gray. If a grid is colored at random, what is the probability that there is at least one $2\times2$ square of just black squares? Here's my attempt at a solution: There are…
Math
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Which threshold maximizes the expected size of the final sample?

For $c>0$, sample repeatedly and independently from $(0, 1)$ until the sum of the samples exceeds $c$. Let $\mu_c$ be the expected size of the final sample. For which $c$ is $\mu_c$ maximised? It is clear that as $c$ tends to $0$, $\mu_c$ tends…
user35671
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Risk of AIDS Infection - Overestimation?

As an example of a probability misunderstanding, the book "Mathematics Statistics and Data Analysis" by John A. Rice gives the following quote from the Los Angeles Times: "Several studies of sexual partners of people infected with the virus show…
M. McIlree
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Probability - Brick in box

From the set {1, 2, 3, ... 999}, 6 distinct numbers are chosen. These are divided into two groups $a_1,a_2,a_3$ and $b_1,b_2,b_3$. Find the probability that a brick made from the dimensions of group $a$ fits into a box made from the dimensions of…
Aniruddha Deb
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Three points on a circle

If three points are randomly chosen on the boundary of a circle, what is the probability that there exists a diameter of the circle such that all three points lie on the same side of it? I have a solution, but I'm very curious to see how others do…
Matt E
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