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
4
votes
1 answer

Counterexample for r.v does not converge in distribution

Give an example where there exist $C>0, q>2$ such that $\mathbf{E}|X-\mathbb{E}X_k|^{q}\leq C\text{Var}(X_k)^{q/2}$ for all $k$ and $\sigma_n\rightarrow\infty$, yet $(S_n-\mathbb{E}S_n)/\sigma_n$ doesn't converge in distribution. Note:…
nerd
  • 1,457
  • 12
  • 20
4
votes
2 answers

Unimodality and continuity for probability distribution

From Wikipedia about the conditions for the Vysochanskij–Petunin inequality The sole restriction on the distribution is that it be unimodal and have finite variance. (This implies that it is a continuous probability distribution except at the…
Tim
  • 47,382
4
votes
1 answer

Compression of equations and coincidence?

I stumbled across an interesting paper last night. Basically, it tries to see if mathematical equations have meaning by determining how well they "compress" the results. For instance, he says the equation $e^\pi-\pi = 19.9990999...$ is…
Nick
  • 997
  • 1
  • 10
  • 21
4
votes
2 answers

An urn contains 2 white and 2 black balls. Balls are drawn successively at random without replacement.

An urn contains 2 white and 2 black balls. Balls are drawn successively at random without replacement. What is the probability that black ball appears for the second time in the 4th draw? I am trying in this way : There can be 3 possibilities - a)…
DukeLover
  • 157
4
votes
2 answers

Cardinality of the intersection of two random sets

Informal description and motivation I am comparing the output of two search engines. Each engine is searching over the same set of 2,000 documents and returning the top 20 hits. I'm trying to construct a hypothesis test where $H_0$ is the hypothesis…
user237392
4
votes
2 answers

What is the probability that nobody is born in the same month?

You have 12 people in a room, what is the probability that nobody is born in the same month? So far i have: $\frac{12!}{12^{12}}$ but i am not sure if this is right. If anyone could confirm this is the way to go or tell me where i am wrong it would…
spexel
  • 303
4
votes
4 answers

Drawing without replacement - prob. for an Ace followed by an Ace?

Given a standard 52-cards deck: You are extracting cards from the deck without replacement, until you get an "Ace" for the first time. What is the probability that the next card will be "Ace" too? I've already seen the following Q&A: Probability of…
Dor
  • 1,074
4
votes
1 answer

How can I convert this percentage into odds?

How can I convert the percentage 0.000007151123842% into odds, so the outcome would be 1 in 13983816. Basically, I am looking for a way to convert any positive percentage into odds so the outcome gives me 1 in N.
Jürgen
  • 121
4
votes
1 answer

What probability would you assign to India's win?

Karan tells truth with probability $\frac 13$ and lies with probability $\frac 23$. Independently, Arjun tells truth with probability $\frac 34$ and lies with probability $\frac 14$. Both watch a cricket match. Arjun tells you that India won, Karan…
Romy
  • 279
4
votes
2 answers

How to find the probability of a family having two boys out of three?

How do I find the probability of a three children family having exactly two boys given that at least one of their children is a boy? Do I use the dependent formula $$P(A \text{ and } B) = P(A) \times P(B \text{ given that }A \text{ has occurred})$$…
4
votes
2 answers

Find the probability of $P_1$ winning the championship

Two players $P_1$ and $P_2$ are playing the final of a chess championship,which consists of a series of matches.Probability of $P_1$ winning a match is $\frac{2}{3}$ and that of $P_2$ is $\frac{1}{3}$.The winner will be the one who is ahead by two…
learner_avid
  • 1,691
4
votes
2 answers

If $S_2$ reaches the semi-final then the probability that $S_1$ wins the tournament is $\frac{1}{20}$

In a knockout tournament $2^n$ equally skilled players;$S_1,S_2,...,S_{2^n}$ are participating.In each round players are divided in pair at random and winner from each pair moves in the next round.If $S_2$ reaches the semi-final then the…
diya
  • 3,589
4
votes
2 answers

I have a bag containing N coins. What is the probability that I have a round dollar amount?

In my country we have \$0.10, \$0.20, \$0.50, \$1, and \$2 coins. If I were to pour a bag of coins out on the table what would be the probability that I could buy a heap of \$1 snacks without needing any change? Does this change if the bag doesn't…
Knells
  • 143
4
votes
1 answer

Using Chebyshev's inequality to obtain lower bounds

I need help with a question I found in Master Stats. I'm unaware of Chebyshev's inequality hence I can't do this question, can anyone help. Q) A company produces planks whose length is a random variable of mean 2.5m and standard deviation 0.1m. Use…
4
votes
4 answers

Probability that the equation $x^2 + k_1 x + k_0 = 0$ has real solutions

$k_1$, $k_0$ are random integer numbers between $1$ and $100$ (including $1$ and $100$, and uniformly distributed). What is the probability that the equation $x^2 + k_1 x + k_0 = 0$ has real solutions? This is a subproblem of another problem, and…
VividD
  • 15,966