This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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4answers
405 views

Probability question with balls in box

Change question title if you can come up with better one In box we have $k$ white, $m$ blue and $n$ red balls. From the box one after another we fetch all balls and we write down color of that ball. ...
4
votes
2answers
940 views

What's the probability that there's at least one ball in every bin if 2n balls are placed into n bins?

I've been working on this all day long. Here's what I've done until now.The denominator is easy. It's $n^{2n}$. I compute the numerator as follows. All $n$ bins have at least one ball = $n$ bins ...
0
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0answers
49 views

Finding out whether or not two graphs are “close”, given 20 points on each graph whose Xs do not match

Let's assume we have two graphs where: Each graph has 600 points per minute. We're allowed to get only one point per minute. We do not get the same point per minute in both graphs. So for example, ...
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1answer
6k views

How to find probability density functions?

$X$ is a random variable uniformly distributed on the real interval [0,1]. Through some experimentation, I found that the probability density function, PDF of: $X$ is $1$ or $\dfrac{d}{dx}X$ $2X$ ...
0
votes
1answer
200 views

Is it possible to derive the CDF of $Z$?

Assume that $X_i$, $Y_k$, $i=0,\ldots,N$, $k=1,\ldots,K$ are non-negative independent non-identically distributed random variables. Let us define the random variable $Z$ as \begin{align} ...
2
votes
1answer
88 views

What is the probability that a multiple of $864$ is divisible by $1944$

If a positive integer multiple of $864$ is chosen randomly, with each multiple having the same probability of being chosen, what is the probability that it is divisible by $1944$?
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1answer
74 views

Pool of $N$ ranked items, pick $P$ at random; chances of selecting 3 of top 5 ranks?

I have $N$ items with a number on them, ranked $1,2,3,4,5,\dots,N$, and I select $P$ items at random. What are the chances that 3 of the top 5 numbered items are in the $P$ chosen items?
6
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3answers
207 views

Number Theory and Probability Question

Compute the probability that a randomly chosen positive divisor of $10^{99}$ is an integer multiple of $10^{88}$
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3answers
220 views

Why doesn't integrating infinitesimally small likelihoods work in this sense?

We know that something is going to happen after $x$ amount of time, but the exact time at which the event occurs is random within $x$ time. (Like, say we did it a bunch of times where it happened in ...
2
votes
3answers
1k views

Keeping track of how to calculate probability/permutations/combinations?

I'm absolutely terrible at calculating these things and I would like to, especially with SATs coming up, improve my capabilities. What always gets me is that there are so many types of ways to ...
2
votes
1answer
351 views

Conditional probability and independent events.

In a test, an examinee either guesses or copies or knows the answer to a multiple-choice question with four choices, only one answer being correct. The probability that he makes a guess is ...
1
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4answers
339 views

Expected lifetime of system that fails with probability $p$ per week

If the probability that a given system fails in a week is p, what is the expected lifetime of the system? I have no clue how to approach this. I have been thinking about this for a while now. ...
1
vote
1answer
116 views

How do i scale my errorbars when i scale my data?

I am plotting distributions of data with the standard deviation and median of my data. Now when i want to scale my median by a another variable, how do i need to modify the standart deviation?
0
votes
1answer
281 views

Expected value for the number of goals in a game

I'm trying to use odds data from bookmakers to estimate the expected number of goals in a game. We have these known facts: P(o4.5) = 0.573 P(o5.5) = 0.458 P(o6.5) = 0.279 P(o4.5) is the ...
5
votes
2answers
699 views

The definition of independence is not intuitive

In the book "Introduction to Probability" by J. Charles M. Grinstead and Laurie Snell independent events are introduced in the following way: "It often happens that the knowledge that a certain event ...
3
votes
2answers
562 views

Why do we need (the abstract concept of) random variables (in discrete probability models)?

What we defined: Suppose we have a (discrete) probability model $\left(\Omega,P\right)$, where $P$ is the probability function (at least, that was the way it was introduced in a course I took; that ...
1
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1answer
2k views

How do you calculate probability of rolling all faces of a die after n number of rolls? [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die Probability of picking all elements in a set Im pretty new to the stackexchange, and posted this is statistics, and then ...
1
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2answers
247 views

Combining independent probabilities of an event

Say $d+1$ independent, equally reliable experts give you probabilities $p_0,\ldots,p_d$ of an event A occurring. What should you think the probability of $A$ is? I'll give my solution (Edit: I ...
1
vote
1answer
110 views

Probability on a nonperfect die

Let there be a nonperfect die with the numbers $1$ to $6$ on its faces. It's known that all even numbers have the same probability to face up and the all odd numbers have the same probability ...
2
votes
1answer
1k views

Statistics: drawing 5 cards - probability for a pair and triplets

I have to apologise if this question has been asked and answered in the past; if there is one field of Mathematics that I struggle to understand, it's definitely statistics. I'm to calculate the ...
0
votes
2answers
1k views

Probability of an even sum

In a set of numbers there are 5 even numbers and 4 odd numbers. If two numbers are chosen at random from the set, without replacement, what is the probability that the sum of these two numbers is ...
0
votes
1answer
290 views

Discrete Random Variable Transformation

i have a problem and i can't figure out any solution. Suppose i have this game: i throw a die untill i get a 6. Every time i throw the dice i pay -1 and when i get the 6 i win 5. (Nb: when i obtain ...
2
votes
1answer
874 views

A probability game involving dice

Consider two players A and B. Player A rolls a fair, six-sided die $m$ times and notes the highest number on the upper face out of all of the rolls. Player B rolls the same die $n$ times and notes ...
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3answers
1k views

Conditional Probability Problem (drawing chips from an urn)

"An urn contains one white chip and a second chip that is equally likely to be white or black. A chip is drawn at random and returned to the urn. Then a second chip is drawn. What is the probability ...
10
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2answers
225 views

How to estimate the number of articles on Wikipedia using the “random article” function?

There is a Wikipedia-type website of a fixed size of $S$ number of articles. You start at any article on Wikipedia. You then start to press the "random article" button and count the number of times ...
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3answers
377 views

Why doesn't this conditional probability equation hold

This is probably a very stupid question but I can't wrap my head around it. $$ P(B \cap A) = P(A \cap B) = P(B \mid A)\cdot P(A) + P(A \mid B)\cdot P(B) $$ Can someone explain intuitively why the ...
0
votes
1answer
334 views

conditional probability of normal random variables

I have the following set of equations: $$ y = \alpha x + \epsilon $$ $$ z=\beta y + \mu $$ and $\epsilon$ is N(0,$\sigma_{1}^2$), $\mu$ is N(0,$\sigma_{2}^2$) and $x$ is N(0,1) and they are all ...
1
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1answer
159 views

Prove conditional probability relation of random variables

Let there be three random variables $X$, $Y$ and $Z$. How can I prove the folowing? $P(X|Y) = \sum\limits_{z} P(X,z|Y)$
2
votes
1answer
145 views

Is this moment inequality valid?

$X$ is a positive continuous random variable. $E[X^p]$ is the $p$-th moment of $X$, $p\ge2$. Is the following moment inequality valid? $E[X^p]\le (p-1)^{p/2}(E[X^2])^{p/2}$ If so, What is the name ...
0
votes
2answers
2k views

probability of sequential events

something has to travel from A to B. between these points there are two stages, where at each one it can fail with a probability of 0.3. what is the total probability that the thing successfully ...
4
votes
3answers
785 views

Is it a characteristic function?

Can anyone explain, how can I prove either $\phi(x) = |\cos t|$ is characteristic function or not? And which random variable has this characteristic function? Thanks in advance.
0
votes
1answer
115 views

Sufficiency for being a probability density function

Once my professor told us in passing that a non-negative integrable (Riemann or Lebesgue) function that integrates to one over its support need not be a probability density function. I have since ...
2
votes
3answers
383 views

What's wrong with my solution for the birthday problem?

So what I decided to do is to start a small case with only 3 people. There are three possible combinations that I could pair up the people, using the symbols A, B, and C to represent the persons ...
0
votes
1answer
124 views

Bounds of joint PDF problem

I'm working on a problem where $f(x,y)=c(x+y)$ is a joint PDF where $0<x<y<1$. Can someone explain what the region $0<x<y<1$ would look like, or how I can integrate with these ...
1
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1answer
245 views

How to find the conditional expectation for this pdf

If $f(x_1,x_2)= {x_1 \choose x_2}(1/2)^{x_1}(x_1/15)$ where $x_2 = 0,1,\ldots,x_1$ and $x_1 = 1,\ldots,5$, how would you find $E[X_2]$ and $E[X_2|X_1=x_1]$ Attempt: To find $E[X_2]$ you just perform ...
2
votes
1answer
315 views

Binary random variables event-level independence implies random variable independence

Can you help me in proving the following? For two binary random variables X and Y, the event-level independence ($x^0 \perp y^0$) implies random variable independence $ X \perp Y$.
2
votes
2answers
115 views

Probability Combinatorial related; choosing couples

7 girs and 3 boys are divided to couples, order within a couple and between couples is not important, what is the probability that one of the couples contains 2 boys? i had this exercise in my ...
0
votes
2answers
311 views

probability coin toss

I am working on some homework questions and I am done everything except this one last question which I am stuck at. I am uncertain of how I can explain or find the probability in this case. I had a ...
6
votes
7answers
10k views

Is it better to play 1 dollar on 10 lottery draws or 10 dollars on one lottery draw?

If I had 10 dollars to spend on a 1 dollar lottery draw, would I have more chance of winning if I spent all 10 dollars in one draw or bought 1 dollar tickets for 10 separate draws? Edit: in terms of ...
1
vote
1answer
448 views

How do you determine the probability of rain over an interval of days?

This may be a basic question, but if there is a twenty percent chance of rain each day for 10 days, what is the probability that it will rain at least once in that 10 day interval? I don't really ...
1
vote
1answer
297 views

Expectation of quadratic form

I have a random sample of size 3 denoted by X below and it comes from a normal distribution with mean 7 and variance 14. I have the matrix A shown below. I am looking for E[Q]. I know that E[Q] = ...
0
votes
1answer
95 views

understanding the solution for “Expectation of the difference of sums”

I found the question Expectation of the difference of sums on this site, and I am trying to understand the solution, which uses the variance of the vector $a$. Please help me to understand the ...
7
votes
3answers
948 views

What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?

Similar to: "What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?" but we allow repeats so 1,1,2,2,3,4,4,4,4,5,5,6 would count. My answer (or simulation) is flawed as I ...
1
vote
2answers
924 views

How do I find the sampling distribution for variance from sampling distribution of $\bar{X}$?

Suppose some people are asked to each randomly pick 30 apples and put into a bag. In this case, the weights of all the bags will surely be different because different apples weigh differently. So ...
-2
votes
1answer
115 views

conditional distribution X_1|X_1+X_2=r

suppose $f(x_1,x_2)=p^2q^{x_2},\ x_1=0,1,\ldots,x_2,\ x_2=0,1,2\ldots$ how can find $\mathbb{Pr}(X_2-X_1\leq1)$? also if $(X_1,X_2,X_3)\sim M(n,P_1,P_2,P_3)$ find conditional distribution ...
6
votes
2answers
946 views

What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?

If I have a fair die and throw it until I get a run of 1,2,3,4,5,6 in order, how many times on average must I throw the dice?
0
votes
3answers
425 views

Find Probability that a player will win Nth match

Please help me with this question: Player "A" starts the first game. Player who starts a game has probability "P" of winning that game. Player who loses starts new game. Assuming this series ...
0
votes
1answer
104 views

What are the $X_1, X_2, …, X_n$ in the Sampling Distribution of $\bar{X}=\frac { 1 }{ n } \sum _{ i=1 }^{ n }{ X_{ j } } $?

The sampling distribution of $\bar{X}$ defined in a book that I am reading is $\bar{X}=\frac { 1 }{ n } \sum _{ i=1 }^{ n }{ X_{ j } } $. I know $X_1, X_2, ..., X_n$ are random variables. But what is ...
1
vote
1answer
125 views

In search of memorable example of “(Pearson-)uncorrelated $\not\Rightarrow$ independent”

I am looking for an easy-to-remember (and non-trivial) example that vividly illustrates that the "uncorrelatedness" (in the sense of Pearson) of two random variables $X, Y$ does not imply that $X$ and ...
1
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0answers
178 views

Conditional independence

Need some help with this exercise (Exercise 4.1 Probability Theory, E.T.Jaynes): Suppose that we have vectors of events $\{H_1,...,H_n\}$ and $\{D_1,...,D_m\}$ which satisfy: (1) $P(H_i H_j)=0$ for ...