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
67 views

What is the probability of drawing 3 balls such that none of them is red?

Given a bag containing $8\ \color{red}{red}$ balls and $4\ \color{green}{green}$ balls, what is the probability of drawing $3$ balls at random such that $\mathbf {none}$ of them are ...
0
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1answer
37 views

Expected % of heads flipping coins of different odds

So this is an analogy for a real world example but for simplicity. So if I were to flip a normal coin ten times I would expect heads 50% of the time or 5 head results. I could then compare this to the ...
11
votes
4answers
1k views

Minesweeper probability

I ran into the situation pictured in the minesweeper game below. Note that the picture is only a small section of the entire board. Note: The bottom right 1 is the bottom right corner tile of the ...
0
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2answers
61 views

Probability that distance of two random points within a sphere is less than a constant

Two points are chosen at random within a sphere of radius $r$. How to calculate the probability that the distance of these two points is $< d$? My first approach was to divide the volume of a ...
-1
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0answers
11 views

Sampling of a changing mixture model

Let f, g, and h be probability density functions, and X, Y and Z be random variables respectively following f, g and h. The mixture model: ${\text h = \frac{f + g}{2}}$ states that the distribution ...
5
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3answers
61 views

Doubt about a probability excercise

I'm a statistics teacher at a college. One day a student came with a doubt about an exercise about probability. The text goes like this: A person has two boxes $A$ and $B$. In the first one has ...
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votes
1answer
17 views

Random Permutation Polynomial With Fixed Inputs

Assume we pick uniformly random a permutation polynomial, $T$, of degree one. we define all polynomials over $\mathbb{Z}_P$. We have fixed inputs $x_i$ (e.g. $x_i \in [1,100]$) My Question: Is ...
0
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0answers
27 views

Calculating Combinations / Permutations [closed]

How do I calculate the number of outcomes as a whole of a series of individual tests with there own outcomes? For example, the best description I could think of would be: There are 10 tests and each ...
1
vote
1answer
22 views

Double integral proving that a function is a probability density

If $$g(x,y)=f(x+y)/(x+y)$$ for $x,y>0$ and $$\int_0^{\infty} f(z) \, dz = 1$$ How do you show that $$\int_0^{\infty} \int_0^{\infty} \frac{f(x+y)}{x+y} dx \, dy = 1$$ as well?
2
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0answers
21 views

Uniqueness of the transformation turning random variables into IID uniform

We have two random variable $X:\Omega \to \mathbb R $ and $Y: \Omega \to \mathbb R^d, d \in \mathbb N$, $F_Y$ is the density function of $Y$ and $F_{X|Y=y}$ is a regular density function of $X$ ...
1
vote
1answer
60 views

Properties of independence and conditional independence

Recently, I see some properties from conditional independence wiki page https://en.wikipedia.org/wiki/Conditional_independence I don't quite understand the properties of "Rules of conditional ...
1
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0answers
23 views

Convolution of independent but 'different' probability distributions

I have the following two probability distributions they relate to a particular ice-cream: ...
0
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0answers
19 views

Compute distribution in Hidden Markov models

Let $Z_1, Z_2, ..., Z_n$ be the latent variables, and $X_1, X_2, ... X_n$ be the observed ones in a hidden markov models. Let's assume that the parameters of the hidden Markov models are known: the ...
0
votes
3answers
76 views

Can someone give me real world example of uniform distribution [0,1] of a continuous random variable.

Can someone give me real world example of uniform distribution [0,1] of a continuous random variable, because I could not make out one.
0
votes
0answers
19 views

what is the intuition behind the SRSWOR formula?

I earlier asked about Slovin's Formula, and learned shortly thereafter that it was derived from this formula. $n=\dfrac{n_0}{1+\dfrac{n_0}{N}}$, Where $n_0=\dfrac{z^2p(1-p)}{e^2}$. So, breaking it ...
0
votes
0answers
21 views

Distributions of identical and distinct objects [closed]

I'm having an issue figuring this problem out. I'm not sure how I should go about it exactly, all I know is that it needs to divided into stages, each its with its own set of cases. So here's is ...
1
vote
3answers
76 views

How to calculate the limit of $(\frac{x}{x+1})^x$

I am looking at the probability of losing $x$ games in a row, in a game where the probability of winning is $1/x$. (For example, if this is a fair casino game, what is the probability of losing $x$ ...
0
votes
0answers
21 views

Probability of me being one of a group

I've heard that in a certain country with a population of about 140,000,000, 200 people become missing on a daily basis. If I want to calculate the random probability that one of those people would ...
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votes
0answers
17 views

what is formula to this eqution [(256)16]1/32+[(169)6]1/12 [closed]

how to solve this equation [(256)16]1/32+[(169)6]1/12 what is formula of this? What is the closed form expression for this? What is the right domain for this Hamiltonian 2? what is the right ...
0
votes
1answer
21 views

Conditional Probability Equivalence

I am reading this paper here: http://www.utm.utoronto.ca/~weisber3/articles/SobervBJPS3.SP.pdf which claims on page 10 that $p(E \wedge [H_x \wedge \sim R]) + p(E \wedge [H_x \wedge E])= p(H_x \wedge ...
0
votes
2answers
29 views

Convergence Events with States

Ignatz repeatedly rolls a fair $6$-sided die. What is the probability that he rolls his first $5$ before he rolls his second (not necessarily distinct) even number? I don't know what to do about the ...
1
vote
1answer
26 views

3 Events, Conditional Independence

Given $A,B,C$ such that: $$ P(A\mid B),P(A\mid B^c),P(B\mid C),P(B\mid C^c) \text{ are known } $$ and that $A,C$ are conditionally independent given $B$, so that: $$ P(A\mid B\cap C)=P(A\mid ...
2
votes
3answers
73 views

How do mathematician make sense of “outcome” and “events” in probability?

One of the biggest challenge for me to understand probability is to make sense of this concept of outcomes and events. To put it plainly, it just doesn't feel like mathematics anymore when we talk ...
0
votes
3answers
52 views

Intuitive meaning of the probability density function at a point

I understand how to integrate probability density functions to find probability within a certain range. However, what I don't understand is what it would mean to set the variable (say x or y) to a ...
-2
votes
1answer
36 views

What time should Celia aim for in her sixth race to make the team? [closed]

To be on the 1-km race team, Celia must have a mean time less than 5 min 50 sec in her 6 tryout races. Her times in 5 races are: 6 min 2 sec, 5 min 53 sec, 5 min 45 sec, 6 min, and 5 min 34 sec. What ...
1
vote
1answer
22 views

When randomly distributing n points amongst m people, what are the odds that one certain person will get a certain amount of points?

I'm mostly curious about how to find this in general, but the actual problem is with 20 points and 5 people. I know probability problems are very counterintuitive, and thus I was unsure after ...
0
votes
1answer
32 views

Probability with $n$ successes before $m$ failures

Independent trials resulting in a success with probability $p$ and a failure with probability $1 − p$ are performed. What is the probability that $n$ successes occur before $m$ failures? Given ...
0
votes
2answers
24 views

Mathematical Backing for Observations seen in Adding Independent Random Variables Together

So I have a function Y = F(N) that takes as an argument an integer number N and returns a summation of N sine-waves of different random parameters. I have plotted the results of two function calls ...
0
votes
0answers
34 views

Probability, expected frequency and resultant distribution skewed or not?

A population consisting of a certain proportion of defective items has mean $\mu = 2$. If a sample of 4 items is examined and repeated 200 times, obtain a) probability of an item being defective, ...
0
votes
2answers
27 views

defective component and probability

An electronics industry uses three plants from A, B and C in the ratio of $3$ to $2$ to $1$. However $1\%$ of components manufactured by A, $2\%$ of components manufactured by B and $3\%$ of ...
0
votes
2answers
28 views

Games and statistics

Three individuals A, B and C alternate in contention of a game according to the following rules: A plays with B and the winner plays with C. The game continues until one of the individuals to win two ...
2
votes
1answer
43 views

Coupon collector problem with $k$ distinct coupon sets to complete

In the standard coupon collector problem we have an urn with $n$ different coupons, from which coupons are being collected, equally likely, with replacement. Simple analysis shows that the expected ...
1
vote
1answer
25 views

Finding conditional probability using Baytes formula

Suppose that chips for an integrated circuit are tested and that the probability that they are detected if they are defective is $0.95$, and the probability that they are declared sound if in fact ...
3
votes
0answers
32 views

Maximum difference between tails in absolute value

I toss a fair coin $n$ times. Some notation: $S_i=$ difference between #heads and #number of tails after the first $i$ tosses, $1\leq i\leq n$. $M_n=\max(S_1,S_2,\dots,S_n)$, ...
0
votes
1answer
48 views

Probability that AJ is guilty

A crime has been committed by a solitary individual, who left some DNA at the scene of the crime. Forensic scientists who studied the recovered DNA noted that only five strands could be identified and ...
0
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0answers
5 views

Concentration bounds on Pearson correlation matrix

I am interested in (rather sharp if not the finest) tail/concentration bounds for the Pearson correlation matrix: let $X_1,\ldots,X_N \sim \mathcal{N}(0,1)$ be correlated random variables; let ...
2
votes
1answer
46 views

Error in Billingsley?

Problem 8.25 in the third edition of Probability and Measure by Billingsley (1995, p. 142) is as follows: Suppose that an irreducible [Markov] chain of period $t>1$ has a stationary ...
1
vote
2answers
43 views

Probability that among 3 random digits two different one

I have been trying to solve the following problem: What is the probability that among 3 random digits, there appear exactly 2 different ones? The formula for no repititions is: ...
1
vote
1answer
45 views

Age distribution when meeting

I have a question regarding Poisson process. I will tell the story in the context of a player-monster game. Consider a player who is born at $t=0$. He will win the game if he can survive until ...
3
votes
2answers
38 views

Selecting k distinct numbers from an array with increasing probability distribution

I have to select k distinct numbers from an array such that probability of a number getting selected is more if it is at the end of the array (probability increases linearly). I'm thinking of ...
1
vote
1answer
30 views

Chessboard pawns arrangement clarification

I have a 8 X 8 chessboard, and 8 identical pawns. These pawns are arranged at random. What is the probability that the pawns are arranged in such a way that each row and column have only one pawn? My ...
3
votes
1answer
56 views

rolling a single die ten times

I have the following problem on a homework assignment for my Probability theory course: You roll a single six sided die ten times. What is the probability that you roll four 1's, three 2's, and three ...
0
votes
0answers
31 views

Conditional distribution

One point is chosen at random in the square $Q=\{|x| + |y| \leq 1\}$. Let $(X, Y)$ coordinates that point. a) The random variable $X$ and $Y$ are independent ? b) Find the density of $X$ given that ...
0
votes
2answers
28 views

Simplifying with Summation

This is a problem out of my statistics book but my issue is simplifying from Step 3 to Step 4 below: Step 1: var X=$\sum\:p_i\:(x_i-E[X])^2$ Step 2: var X=$\sum\:p_i[x_i^2+E[X]^2-2x_iE[X]]$ Step ...
0
votes
2answers
30 views

Understanding the geometric distribution

Simple question that has to do with the interpretation of the geometric distribution and frequency function: $P (X=k) = (1-p)^{k-1}p $ for $k = 1,2,3... $ where we are interpreting X as being up to ...
0
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1answer
42 views

Rumor and probability

31 people in a community, a person has a rumor to a second which, in turn, repeats to the third, etc. At each step the person receiving the rumor is randomly chosen among 30 people available. a) Find ...
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2answers
39 views

Two urns, A and B, each with two drawers.

If you have two urns, A and B, each with two drawers. The urn A has a gold coin in a drawer and a silver coin in the other drawer while the urn B has a gold coin in each drawer. An urn is chosen at ...
-1
votes
1answer
57 views

How many steps would it take to get to the top of this staircase?

There are 26 steps in a staircase. You have a 51% chance to step onto the next step, and a 49% chance to step back down to the step prior. Assuming you are already on the first step, how many steps ...
0
votes
3answers
28 views

Dice roll - Geometric Distribution Question

I am having a hard time understanding the concept of a negative binomial distribution. For example the question: How many times do you expect to roll a six-sided die before landing on the number ...
1
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0answers
30 views

Uniformly boundedness of convolutions

Assume $X$ is an absolutely continuous random variable with pdf $f:\mathbb{R}\to[0,\infty)$. Assume further there exists $M>0$ s.t. $|f(t)|\leq M \quad\forall t\in\mathbb{R}$. Let $X_1,\dots,X_n$ ...