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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1answer
15 views

What are the odds of spinning matching items in a slot machine?

Lets say we have a slot machine with 5 reels. Each reel has 5 different items on it. What are the odds of spinning 2, 3, 4 and 5 matching items? As I understand the probability of rolling a ...
2
votes
2answers
15 views

Combinatorics question on group of people making separate groups

If there are $9$ people, and $2$ groups get formed, one with $3$ people and one with $6$ people (at random), what is the probability that $2$ people, John and James, will end up in the same group? ...
0
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1answer
26 views

Probability of Team A winning where a draw is not allowed

I have the probabilities for a range of final scores for a sports team A and also for a sports team B. I assume that these probabilities are fixed and not affected by outside factors including the ...
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0answers
23 views

Additional Problems about conditional expectations

When I was a student, I was able to solve these problems, but now I can't because I forgot some important things. If you show me the solutions to at least two of them, I am sure, I will refresh it all ...
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3answers
41 views

Prove that if $A$ is independent of $B$, $A$ is independent of $C$, then $A$ is independent of $B\cup C$.

Prove that if $A$ is independent of $B$, $A$ is independent of $C$, then $A$ is independent of $B\cup C$. $\mathbb{P}(A)\mathbb{P}(B)=\mathbb{P}(AB)$ $\mathbb{P}(A)\mathbb{P}(C)=\mathbb{P}(AC)$ So ...
-1
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0answers
22 views

Four Conditional Expectation Problems

I can't solve these problems and I will be very grateful to you for your help: 1) The random variables $X$ and $Y$ are independent and both have a uniform distribution $U([-1,1])$. Find ...
0
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0answers
27 views

Bookmaker's odds

Suppose a match can be completed in three ways: win, loose or draw. A bookmaker provide the following coefficients (including spread) for each case respectivelly: $c_1, c_2, c_3$. That is, if a player ...
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0answers
32 views

Biased Random Walk with Variable Probability

Consider a random walk in which the probability to move forward in time $t$ is $p_t$ and the probability to move backward is $q_t=1-p_t$ with $p_t<q_t$ with $p_t<p_{t+1}$ and $q_t>q_{t+1}$. ...
0
votes
2answers
22 views

Simple sequence of experiments

If I have an experiment with $\frac{1}{2}$ probability of success, how many times I have to run as to be 99.9% sure I am successful? Is someone please able to explain how to resolve this step-wise? ...
0
votes
1answer
13 views

How to determine if events are mutually independent.

Consider the experiment of tossing three coins. Let A be an event of getting head on the first coin, B be an event of getting tail on the second coin, and C be an event of getting at least two heads. ...
0
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3answers
24 views

Uniform PDF for continuous variable, why does the probability values increase to 1, when its normalized?

Consider a "spinner": an object like an unmagnetized compass needle that can pivots freely around an axis, and is stable pointing in any direction. You give it a spin and see where it comes to rest, ...
1
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2answers
37 views

Fundamentals of Probability

Suppose I have two boxes , containing white and black balls. In the first one , we have 8 white and 6 black balls. In the second one , we have 4 white and 7 black balls. Now if one ball is drawn at ...
0
votes
1answer
24 views

Expectation finite in probability

With p < 2, why the following last expectation is finite? we have $N(t)=\#{ \lbrace n \geq 1:|{b_n}| \leq t \rbrace }$; $\underset{t\to \infty}{\mathop{\lim \sup }}\,N(t)/t^p < \infty$ for ...
0
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2answers
28 views

Classical Probability

There are three buttons which are painted red on one side and white on the other. If we tosses the buttons into the air, calculate the probability that all three come up the same color. Remarks: A ...
0
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1answer
11 views

inequality probability between order statistics of two independent distribution

Suppose we have two independent distributions $F_1$ and $F_2$ and from each distribution, we draw $k$ variables. Let us represent the $k$ i.i.d. variables from $F_1$ as $\{X_1, X_2, \ldots, X_k\}$. ...
0
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0answers
32 views

calculate the cdf

The continuous random variable $R$ has the following probability density function on the sample space $−1 \le r \le 1$, $$f(r)=\begin{cases} \frac{1}{4} \hspace{.5cm} \text{for} \hspace{.5cm} −1 ≤ r ≤ ...
2
votes
1answer
40 views

Does $X ⊥ Y \leftrightarrow X ⊥ Y | Z$ implies $(X,Y) ⊥ Z$?

Let $X, Y$ and $Z$ be random variables. Let $p_1$ be the statement that $(X,Y) ⊥ Z$ (meaning $(X,Y)$ and $Z$ are independent), $p_2$ be the statement that $X ⊥ Y$ (meaning $X$ and $Y$ are ...
-2
votes
1answer
33 views

Statistics question from test! Please help… [on hold]

A certain flight arrives on time $93\%$ of the time. Suppose $195$ flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that: a) exactly ...
1
vote
1answer
31 views

apply the law of total expectation

I'm a little bit confused about applying the law of total expectation. Suppose $v_1,v_2,v_3$ are three random variables drawn independently from the same distribution $\mathrm{uniform}(0,1)$, which ...
0
votes
0answers
27 views

Counterexample for $(Y_1 \perp Y_2) \mid (X_1, X_2) \Rightarrow (Y_1 \perp Y_2) | X_1$?

Let $(Y_1 \perp Y_2) \mid (X_1, X_2)$ mean that random variables $Y_1$ and $Y_2$ are conditionally independent on $(X_1, X_2)$. Either is there a counterexample for $(Y_1 \perp Y_2) \mid (X_1, X_2) ...
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0answers
21 views

Confidence interval for differenciation

I will also ask the question here, because I realized it can also be a logical/probability problem. I'm a chemist so my question will be experience-oriented. Lets' say I have 5 molecules (A, B, C, D, ...
0
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0answers
23 views

Probability Density following affine transformation

Suppose $X$ is a random variable in $R^n$ and $Y=a^{T}X+b ∊ R$. If $f_X$ is the density of $X$, then what (and how!) can I obtain $f_Y$ the density of $Y$? It is assumed that $a\neq 0$. I saw the ...
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0answers
33 views

What is the Cumulative Distribution Function of $a/x^b$? [on hold]

I was just wondering what the CDF of $$\frac{a}{x^b}$$ would be? $a$ and $b$ are positive constants and $b \gt 1$ ($1.22$ to be exact). $x \in [0, \infty)$ theoretically but in practice once $x$ has ...
1
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2answers
24 views

Probability of single digits from coin tosses

Let's say that I wanted to generate 4 random numbers using a coin toss. I could toss the (unbiased) coin 4 times to generate one of 16 possible numbers (e.g. TTHH=0011=3) and just ignore any results ...
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0answers
23 views

Finding n for a given P of a Bernoulli trial

I'm randomly sampling $N$ items and I want to find $n$ such that I have a probability $P$ that I'll miss one. Practically, I'd select $P$ to be something like $10^{-12}$ so I'm almost assured to ...
2
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0answers
41 views

Probability of an Indisputable winner at Texas Holdem

What are the fraction of hands that can be classified as "indisputable winners" after the river is revealed in Texas Holdem? An indisputable winner is a hand that cannot lose. A clear example would ...
2
votes
3answers
47 views

Adding two discrete distributions

I am taking a probability course and I am having trouble adding two discrete distributions. The two distributions given are: $X$ has a discrete uniform distribution on the integers $0,1, ... ,9$. ...
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votes
1answer
30 views

Russian Roulette consecutive bullets

You are playing a game of Russian Roulette. If instead of one bullet, two bullets are randomly put in the chamber. Your opponent played the first and he was alive after the first trigger pull. You ...
0
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0answers
28 views

Conditional Probability Error Question [on hold]

Let $P_0 = 0.25,$ $P_1 = 0.35$, $P_2 = 0.25,$ and $P_3 = 0.15.$ What is the probability of more than one error? I thought to sum $P_1, P_2, P_3$ together but that doesn't seem to work. What formula ...
0
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1answer
14 views

Query about non-singular transformation of vectors

Suppose we are given a probability function, P (x^T (Y-z)≥0) , where ‘x’ is a vector, ‘Y’ is a random variable and ‘z’ is a known value. Now, suppose, we make a non-singular transformation w=Ax, ...
0
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0answers
14 views

a problem involving binary entropy function

let $\alpha<1/2$ such that $2^{H(\alpha)}\le 2^{1-\epsilon}$,when $H$ is binary entropy function. how can i prove that then we have: $2^{n(1-\epsilon)}\ge \sum\limits_{i\le \alpha n } {n \choose ...
2
votes
2answers
27 views

Count ways to place $n$ identical balls into $n$ urns so that exactly one urn is empty?

How many ways are there to plane n indistinguishable balls into n urns so that exactly one urn is empty? Why is the answer for this question n(n-1)?
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1answer
30 views

Probability of a combination of two distinct numbers chosen from $1, \dots, 28$ [on hold]

If two distinct numbers are taken from $1,2,3, \dots, 28$, what is the probability that their sum is less than $13$?
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votes
1answer
49 views

Can somebody integrate this function for me? [on hold]

This is the function. $\frac{1}{6.08 \cdot \sqrt{2\pi}}\exp\left(-\frac{(x-10.75)^2}{2 \cdot 6.08^2}\right)$ Thanks in advance!
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2answers
28 views

In a game of poker, what is the probability that a five-card hand will contain… [on hold]

In a game of poker, what is the probability that a five-card hand will contain (a) a straight (5 cards in unbroken numerical sequence) and (b) four of a kind. Solution given for (a) is $10(4^5 - 4)/ ...
1
vote
1answer
12 views

Finding out the percentage points.( F - Distribution).

How to find the values of these $x_1$ and $x_2$ , given , $P(x_1<F_{7,7}<x_2) = 0.90$ , using the F-Distribution tables.. Can anyone provide me a hint for this ?
0
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3answers
25 views

Chance of getting tails in the second throw with abnormal coin.

You have one coin that is normal, and one coin that have "tails" on both sides. Then you choose a coin without knowing which one, and you flip it. You get tails and decide to flip it again, what are ...
2
votes
1answer
44 views

Why is the measure of a boundary of an open ball positive in only a countable number of cases?

Let $X$ be a Polish (complete separable metric) space and $\mathbb{P}$ a Borel probability measure on $X$. Let $x_1, x_2, \ldots$ be a sequence of points dense in $X$. How can you prove that there is ...
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0answers
12 views

Calculating the Shannon information of drawing equal no. of cards

One card is drawn each from a $k$ deck of 52 cards where $k$ is a multiple of $52$. I need to prove that information of an outcome where each card appears the same number of times tends to ...
0
votes
1answer
21 views

Probability - branching

A population starts with 1 member: at t=1 , it can either divide with probability of p or dies with probability of 1-p. If it divides, then both of its children behave independently with the same ...
0
votes
1answer
25 views

Classical Probability and Combinatorics

Shuffle a standard deck of cards and cut it into three piles. What is the probability that a face card will turn up on top of one of the piles? There are 12 face cards (four jacks, four queens and ...
2
votes
1answer
18 views

Statistical bias and the probability of an outcome.

A town referendum has occurred. The question posed to voters was YES or NO on a local law. There were 3 methods of voting: Electronic machine (voting booths), absentee ballot, and affidavit ballot. ...
0
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2answers
25 views

Probability-Bayes theorem

The probability that bulbs are detected faulty if they are defective is 0.95 and the probability that bulbs are declared fine if in fact they are fine is 0.97. If 0.5% of the bulbs are faulty, what is ...
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votes
2answers
35 views

Russian Roulette probability question

You are playing a game of Russian Roulette. If instead of one bullet, two bullets are randomly put in the chamber. Your opponent played the first and he was alive after the first trigger pull. You ...
0
votes
1answer
38 views

to verify a relation involving conditional probability with an example

we have a relation P(A/complement(B)) = (P(A) - P(A/B)P(B))/(1-P(B)). This equation satisfies for A and B except P(B)=1. If X,Z are independent exponential RV with parameter $\lambda$1 = 1/10.39 ...
0
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0answers
15 views

Why distribution of multiple recursive random number generators is uniform?

I was reading the article of L'Ecuyer on random number generation. The title of this article is "Uniform Random Number Generation". One of the proposed PRNGs there, is multiple recursive random ...
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0answers
25 views

How to calculate multiple dice turns?

Assume we have a single dice , with 10 faces. We want the dice to show up "[1] face" 10 times And those 10 times must be arrange one after another. Like this. Startgame .....10 , 2 , 4 , 5 , 1 ...
0
votes
1answer
14 views

Bounding probability based on binary values

I've been reading this paper on probabilistic logic: http://ai.stanford.edu/~nilsson/OnlinePubs-Nils/PublishedPapers/problogic.pdf On page 76 theres a 3d diagram and Nilsson mentions the bounds on ...
1
vote
1answer
27 views

Calculating conditional probability of discrete uniform r.v.

X is a discrete uniform random variable on $\{a, a+1, a+2, ... , b\}$ with mean 7 and variance 4. Find $Pr[X \leq 6| X > 4]$ I'm not familiar with the discrete uniform distribution. I was ...
0
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3answers
39 views

How are probabilities defined?

This stray thought has been bothering me for the past week. It seems that all probabilities and percentages are defined using the extremes 0% and 100%. Where: 0% is the probability that something ...