Mathematics Stack Exchange
Mathematics Stack Exchange

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
17
votes
2 answers

A man who lies a fourth of the time throws a die and says it is a six. What is the probability it is actually a six?

First, I apologise for the vague title. I couldn't think of a short way to represent the problem. Also, I am aware that a similar question exists, but I have a little bit more insight. The problem is: A man is known to speak the truth three out of…
Shreyas
  • 345
17
votes
2 answers

Constructing an $\epsilon$-net of $l_2$ unit ball

I am interested in probabilistic or explicit ways to construct an $\epsilon$-net of the $l_2$ unit ball in $\mathbb{R}^{d}$. I know that, for every $\epsilon > 0$, there exists an $\epsilon$-net $\mathcal{N}_{\epsilon}$ for the unit sphere in $d$…
megas
  • 2,276
17
votes
3 answers

Banach Matchbox Problem

Banach Matchbox Problem: Suppose a mathematician carries two matchboxes at all times: one in his left pocket and one in his right. Each time he needs a match, he is equally likely to take it from either pocket. Suppose he reaches into his…
User
  • 173
16
votes
5 answers

Probability of getting a full house

If five cards are selected at random from a standard 52 card deck, what is the probability of getting a full house. This is what I am thinking. $(52*\binom{4}{3}*\binom{4}{2})/_{52}C_5$ Is that right?
Jaysun
  • 317
16
votes
6 answers

Why is not the answer to all probability questions 1/2.

Ok, I know this is wrong, but I want someone to tell me why. Let's take a normal heads tails example of a fair coin. The probability of getting head = 1/2. And I write this is because, either it will be heads, or not. Hence two cases that makes it…
Kraken
  • 593
16
votes
2 answers

How to compute moments of log normal distribution?

The computed moments of log normal distribution can be found here. How to compute them?
ashim
  • 904
16
votes
1 answer

Expected value of infinite sum

$x_1, x_2, \dots, x_n, \dots$ - independent random variables. Is it true that $$ \sum_{i = 1}^{\infty}Ex_i = E(\sum_{i = 1}^{\infty} x_i) $$ ?
user1761982
  • 317
16
votes
1 answer

Very simple dice game

Two players compete to reach a certain number N of points (for example 100) to win the game by throwing a each roll two regular dice and noting the amount accumulated since their first roll. So, the first player reaching N points wins the game.…
Jean-Pierre
  • 1,043
16
votes
3 answers

What is the expected number of trials until x successes?

This is barely a probability question, but I needed to check to make sure the solution is as simple as I believe it to be. What is the the expected number $n$ of independent trials needed to have $x$ success (not necessary to be consecutive) given…
ovnarian
  • 161
15
votes
5 answers

Two players alternately flip a coin; what is the probability of winning by getting a head?

Two players, $A$ and $B$, alternately and independently flip a coin and the first player to get a head wins. Assume player $A$ flips first. If the coin is fair, what is the probability that $A$ wins? So $A$ only flips on odd tosses. So the…
Thomas
  • 423
  • 2
  • 6
  • 9
15
votes
3 answers

How calculate the probability density function of $Z = X_1/X_2$

Let $X_1$ and $X_2$ be two continuous r.v., my question is: what is the p.d.f of $Z=X_1/X_2$?
Fan Zhang
  • 1,967
15
votes
6 answers

Estimation of $\pi$ using dice

I have been asked in a Quant interview to estimate the value of $\pi$ using dice. I don't know even how to start with. Any help would be appreciated. Thanks.
pikachuchameleon
  • 2,809
15
votes
3 answers

Probability of the union of $3$ events?

I need some clarification for why the probability of the union of three events is equal to the right side in the following: $$P(E\cup F\cup G)=P(E)+P(F)+P(G)-P(E\cap F)-P(E\cap G)-P(F\cap G)+P(E\cap F\cap G)$$ What I don't understand is, why is the…
Hex4869
  • 505
15
votes
3 answers

A game with $n$ players - II

Consider $n$ player numbered $1,2,\ldots,n$. If player $i$ fights against $j$ then $i$ wins with probability $i/(i+j)$. There are no ties. A player $i_1$ is extracted at random. Then, a second different player $i_2$ is extracted at random. They…
user207096
15
votes
2 answers

Applying law of total probability to conditional probability

I was solving problems based on Bayes theorem from the book "A First Course in Probability by Sheldon Ross". The problem reads as follows: An insurance company believes that there are two types of people: accident prone and not accident prone.…
RajS
  • 1,317
1 2 3
…
99 100