Questions tagged [probability]

For basic questions about probability and the questions associated with the calculation of probability, expected value, variance, standard deviation, or similar statistical quantities. For questions about the theoretical footing of probability (especially using [tag:measure-theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

Probability is a numerical quantity which lies in the interval $[0, 1]$. According to the Bayesian view, it represents the belief about an event or preposition and it is interpreted as how likely it is for an event to occur, or of how likely it is for a proposition to be true. According to the frequentist view, it represents the relative frequency of a favourable event with respect to the sample space. Use this tag for basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantities. For questions about the theoretical footing of probability (especially using ), please ask under instead. For questions about specific probability distributions, please use .

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Flip a fair coin until three consecutive heads or tails appear

What is the expected number of flips until three consecutive heads or tails appear?
LittleSweet
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How to describe this structure in spoken words?

$$\large f(0) = P(X = 0) = \frac{\binom{3}{0}\binom{17}{2}}{\binom{20}{2}} = \frac{68}{95},$$ I'm working on annotating math (probability and statistics) for the visually impaired that is to be read aloud by a screen reader and don't know what to…
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Probability that the difference of the max and min of three random numbers between 0 and 2 is less than 1/4?

Three numbers are chosen at random between 0 and 2. What is the probability that the difference between the largest number and the least number is less than 1/4? This is a problem from JHMT Calculus 2011. I'm trying to see if there are any better…
user381493
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Roll a dice infinite times BUT pay $1 to play - strategy?

I am stuck with a question related to the optimal strategy of rolling a dice. Its an extension of the problem "Roll a dice and take either the amount on the dice or re-roll (a maximum of twice)". Heres the link to the basic version and solution: The…
Math525
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Machine Learning: Good book for learning Probability and statistics?

I am trying to learn machine learning and looking for a good book to understand probability and statistics from machine learning point of view and for the sake of understanding probability. Though I have studied probability in the past, I am still…
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Expected number of Pareto-optimal points

Suppose $S$ is a set of $n$ points in a plane. A point is called maximal (or Pareto-optimal) if no other point in $S$ is both above and to the right of that point. If each point in $S$ is chosen independently and uniformly at random from the unit…
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What is symmetry?

In probability, I have often seen the argument "and this probability equals $\frac 1n$ by symmetry" and I have never really understood the formality behind that statement. One of the biggest problems I have had with this line of reasoning is when…
Guacho Perez
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Prove there are no hidden messages in Pi

Assume that a proof that pi is normal existed. Is it then possible that starting at some finite position x in pi, from there on every p(n)'th digit is 0, where p(n) is the n'th prime? I know probability arguments say no, but do they also prove that…
TROLLHUNTER
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Probability of selecting two numbers with a sum of squares divisible by 10

Two natural numbers $x$ and $y$ are chosen at random. Find the probability that $x^2 + y^2$ is divisible by 10. I could not understand how select two numbers from any natural number (infinite).
user123733
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The probability of an ant rarely visiting the points with both coordinates even

A point of the lattice $\mathbb{Z}^3$ in $\mathbb{R}^3$ is painted white if at least one of its coordinates is odd. An ant is moving in $\mathbb{R}^3$. At each integer time $t$ the ant is at a point in $\mathbb{Z}^3$ and it chooses one of points in…
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Dynamic voting quorum

Problem: Suppose that a committee with $n$ members needs to vote on whether to accept a proposition. Each member in the committee can cast a yes/no vote ($q_i\in\{1,0\}$ for $i\in \{1,2,...,n \}$), and each member's vote has a different weight…
OO_SE
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Average minimum distance between $n$ points generate i.i.d. uniformly in the ball

Let $U \in \mathbb{R}^3$ be distributed uniformly in the Ball in $\mathbb{R}^3$ centered at zero. That is $U \sim f_U(u)= \frac{1}{ \frac{4}{3} \pi R^3}$ for all $\|u\|\le R$ where $R$ is the radius of the ball. Now suppose we generate $n$…
Boby
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Conditional probability is undefined even though it seems defined intuitively

We know that conditional probability $P(A | B)$ is undefined when $P(B) = 0$. But this doesn't seem to be true to me always. Consider the probability of chosing a real number between $r$ such that $0 \leq r \lt 1$ where any real number in $[0, 1)$…
Lone Learner
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Drawing two cards from a deck of 16 (4 ranks and 4 suits)

I'm reviewing for an exam and have come across a problem marked incorrect on my homework. The problem reads, There are 16 cards in a deck. The cards have 4 ranks (Jack, Queen, King, and Ace) and 4 suits (Clubs, Diamonds, Hearts, and Spades). You…
Dewick47
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First player to win k matches of series of n, win probability p = 0.5

A series of matches are held between n identical competitors. Each is won by one of the n with equal probability (no ties). I'm looking for a probabilistic description of the outcome when looking at the first player to win 1, 2, ... matches. For…
Charles
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