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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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Proving sets to be independent

I know that I can use P(AB)=P(A)P(B) to prove whether sets are independent. But how can I use this to say that P(A)=0.3 and P(B)=0.4 and P(AUB)=0.6 are or aren't independent? It's fine not to give an outright solution, an explanation would be much…
user7174
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Can one determine the joint distribution of $(X,Y)$ from the probability densities of $X$, $Y$, and $X+Y$?

Can one determine the joint distribution of $(X,Y)$ from the probability densities of $X$, $Y$, and $X+Y$? Here, $X$ and $Y$ are random variables from a sample space $(\Omega, \mathbb{P}) \to \mathbb{R}$. This is NOT a homework question.
user062295
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Probability of eighth best reaching the semifinals

$16$ players $P_1, P_2, ..... P_{16}$ take part in a tennis knockout tournament. The order of the matches is chosen in random. Lower suffix player is better than higher suffix, the better wins. What is the probability that the eighth best reaches…
Sourav Suman
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Maximizing the probability of a urn problem

How can 20 balls, 10 white and 10 black, be put into two urns so as to maximize the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it? Intuitively i know the right answer: put 1 white,…
user2345678
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Is it a coincidence or is there an explanation for this?

Tossing a fair coin $2n$ times. After the $i$-th toss, the number of heads is $H_{i}$ and the number of tails is $T_{i}$. Is this a mere coincidence that the probability of $H_{2k}=T_{2k}$ equals to the probability that $H_{2i}\ne T_{2i}$ for all…
xzhu
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Kullback-Leibler divergence for binomial distributions P and Q

Note: this is an assignment question Let $X$ be a discrete random variable with values in $\{1,...,n\}$. $P$ denotes the distribution on $\{1,...,n\}$ when $X$ ~ $bin(n,p)$ and Q denotes the distribution on $\{1,...,n\}$ when $X$ ~ $bin(n,q)$ for…
Marco
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If two different numbers are taken from the set {0,1,2,3, ......, 10} ...

If two different numbers are taken from the set {0,1,2,3, ......, 10} then what is the probability that their sum as well as absolute difference are both multiples of 4 Here is my work out The sample space here is equal to 55. Now to me the…
Pole_Star
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For two uncorrelated random variables $X,Y$, why does $\rho(X+Y,2X+2Y)=4?$

Given two uncorrelated random variables $X,Y$ with the same variance $\sigma^2 $ I need to compute $\rho= \frac{COV(X,Y)}{\sigma(X)\sigma(Y)}$ between $X+Y$ and $2X+2Y$. I know it should be a number between $-1$ and $1$ and I don't understand how…
Ben Benli
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Which one of these options is false?

Given two independent events $A$ and $B$, with given conditions: $0 \lt P(A) , P(B) <1 $. Which one of the following options is/are false? $A$ and $B’$ are independent. $A’$ and $B’$ are independent. $P(A|B) = P(A|B’)$ For any event c, with $0…
ABcDexter
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meaning multiplying an outcome by its probability

I was reading about the expected value in probability theory. What is the meaning of multiplying an outcome by its probability. For example if I multiply and amount of money by an interest rate I get the iterest amount. What would mean to multiply…
kprincipe
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Expected value of $X^n$

Given: $F_X(x)$ is a CDF and: $E[X] = \int\limits_0^\infty (1-F_X (x))\, dx\ $ How do I prove: $E[X^n] = \int\limits_0^\infty nx^{n-1}(1-F_X(x))dx $
Thomas Sowell
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Probability of choosing same multiple

Will E. Pikett randomly selects an odd integer less than $100$ that is a multiple of $3$. Betty Wont randomly selects an odd integer less than $100$ that is a multiple of $5$. What is the probability that they selected the same number? My…
Ian L
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Bivariate Lognormal Distribution

Is there a pdf for bivariate lognormal distribution? Suppose there are 2 random variable $X_1$ and $X_2$ with standard normal distribution, how would the pdf of a bivariate lognormal distribution look like? Thanks!
alamak
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Confusion with event notation and usage in probability

In $P(E_1, E_2)$, the comma is read as an and. However, consider a random variable with $\Omega=$ {1,2,3,4,5,6} and $E_1$={1,2,3}, $E_2=${3,4,5,6} Am I right in assuming that a comma in the event and sample space definitions means xor? Therefore,…
Wuschelbeutel Kartoffelhuhn
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How would you discover the normal distribution?

What is the simplest or easiest or most clear way that a mathematician could discover the normal distribution and the central limit theorem? The derivation does not need to be rigorous. (Much of calculus was discovered and understood clearly before…
eternalGoldenBraid
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