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
8
votes
1 answer

Probability of an event occurring within a smaller time interval if one knows the probability of occurrence over a larger time interval

The following threads are related to my question, but since I have minimal confidence around probability & math, I'm not sure how to interpret some of this and whether the answers apply to my situation (I think I'm dealing with a binomial process…
Cathleen B
  • 183
  • 1
  • 4
8
votes
1 answer

Efficient sampling of a mixture model

I know there is an easy way to sample standard mixture models if the mixture components can be easily sampled. But, I have a slightly different scenario and I'm wondering if there is an analogous method (or any method at all that is nice). I'll…
RandomGuy
  • 530
8
votes
2 answers

The exact probability of observing $x$ unique elements after sampling with replacement from a set with $N$ elements

Say I sample with replacement from a set of $N$ unique elements s.t. elements are selected with uniform probability. If I sample with replacement $M$ times from this set, what is the exact probability $P(x)$ that I have observed at least $x$ unique…
Wilk
  • 81
8
votes
2 answers

Expected number of times random substring occurs inside of larger random string

I have a four-letter alphabet containing A, B, C, and D. What is the expected number of times a string of length $m$ occurs inside of larger random substring of length $n$, both generated from the same alphabet? I think I've got it so far for an…
Justin Poliey
  • 183
  • 1
  • 6
8
votes
5 answers

Ratio of Boys and Girls

In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)
Jaguar
  • 485
8
votes
4 answers

Probability: A flaw in logic? The emperor's proposition with marbles and two urns

I've tried searching for this question but couldn't find it on stackexchange. This is a common type of interview question; I ran into it doing brain teasers on a probability puzzles app, and if you fine people agree with my logic, I will inform the…
appills
  • 83
8
votes
1 answer

Two groups of numbers with close sums

Let $n$ be a positive integer, and independently randomize numbers $x_1,\dots,x_n,y_1,\dots,y_n$ from $(0,1)$ uniformly. Fix a real number $r>0$. Let $p_n$ be the probability that the indices $\{1,\dots,n\}$ can be divided into two groups $A,B$ so…
pi66
  • 7,164
8
votes
1 answer

What is the probability that $\min\limits_{i}\max\limits_{j} M_{ij}\gt \max\limits_{j}\min\limits_{i} M_{ij}$

Assume you have a $n\times n$ matrix $M$, each entry is filled with a number from $1$ to $n^2$ randomly, and no two entries are the same. There are $n$ rows, select the max number of each row, so there are $n$ numbers. $A$ is defined as the minimum…
fizis
  • 953
8
votes
3 answers

What is the chance of rolling a specific number after a certain amount of rolls?

Say I roll a $6$ sided dice and I want to roll a $6$. what is the probability that I will have rolled the number I want after $6$ rolls? I have been using this: $\displaystyle1-\left(1-\frac{1}{x}\right)^y$ where $x$ is the number of sides and $y$…
8
votes
3 answers

expected number of balls withdrawn to get equal numbers of black and white balls

There are $n$ black balls and $n$ white balls in a bin. I withdraw the balls one at a time without replacement until I have an equal number of white and black balls. What is the expected number of balls that I have to withdraw? It appears that…
keng5
  • 123
8
votes
1 answer

What is the probability that they have no common prime factor?

I am seeking a simple way to solve the following problem. It is an easy problem, but I don't like the way I solve the problem. I listed two sets of numbers and counted one by one first and then find the probability. It works for this problem. But if…
learning
  • 1,749
8
votes
0 answers

What is the probability that the Golden State Warriors will break the NBA regular season record of wins?

There are $82$ games in a regular season, and the current record is held by the Chicago Bulls, at 72-10. As of yesterday (March 4th 2016), the GSW season performance stood at 55-5. Assuming they maintain this record or do better,they need to win at…
KVemuri
  • 89
8
votes
1 answer

Probability of obtaining triangle when choosing $3$ points from $3\times3$ array

$9$ points are placed in a $3\times3$ array. If $3$ points are randomly selected, what is the probability that they are the vertices of a triangle?
Ranga
  • 135
8
votes
3 answers

two integers are chosen at random between $0$ and $10$ what is the probability that they differ by no more than $5$?

I've started studying geometric probability and I am having some difficulty with this version of problem : Two integers are chosen at random between $0$ and $10$ inclusive. What is the probability that they differ by no more than $5$ ? The…
Mr. Y
  • 2,637
8
votes
5 answers

Draw cards repeatedly, until we find the ace of spades. Probability that we draw between 20 and 30 cards?

consider this problem: Draw cards repeatedly, without replacement, from a standard 52-card deck until we find the ace of spades. What is the probability that we draw between 20 and 30 cards? The solution I came across: $$P(A)=\frac{11}{52}$$ where…