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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0
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2answers
25 views

why probability is multiplied in finding out dependent probabilities?

Why is probability multiplied in case of dependent events? When we want to find out say, We take out a card from a deck of 52 cards and take another without replacing, We get the probability of ...
0
votes
0answers
6 views

Existence of Joint Distribution from Overlapping Marginal Distribution

Suppose $x_i\in \mathbb{R}^{n_i}$ for $i=0,1,...,k$. For each $i=1,...,k$, suppose $F_i$ is a probability measure of $(x_0,x_i)$ on $\mathbb{R}^{n_0 + n_i}$. Assume all $F_i$ have the same marginal ...
0
votes
2answers
31 views

Calculating the expectation of binomial distribution without calculating the summation

We know that expectation of a binomial distribution is $$\sum _{1}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){p}^{k}{\left(1-p\right)}^{n-k}k = np$$ But while proving it, it is being written ...
2
votes
2answers
383 views

Three fives dice toss

If four dice are tossed, find the probability that exactly 3 fives will show ( answer to the nearest thousandth in the for 0.xxx)?
1
vote
1answer
41 views

Help with proof that $E(G|a < G < b) \lt E(H|a < H < b)$ for truncated normal distributions

Consider two independent normally distributed random variables with equal standard deviations, $G\sim N (\mu_{G}, \sigma)$ and $H\sim N (\mu_{H}, \sigma)$ that are truncated between points $a$ and $b$....
0
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2answers
19 views

Card Probability Without Replacement

So there are 15 cards total, 5 red, 7 orange, and 3 yellow. At random you pick 3 (no replacement). What's the probability of picking: 1) Exactly 2 Red? 2) Not more than one yellow? 3) One of each? ...
2
votes
0answers
10 views

sampling requirements in probabilistic polynomial identity testing

In the Schwartz–Zippel algorithm for bounded error probabilistic polynomial identity testing, the main theorem is the following: For a non-zero multivariate polynomial $p(x_1,...,x_n)$ of total ...
2
votes
2answers
52 views

Most likely order of independent normal random events

The problem I have is, given $n$ independent normal distributions describing the times that $n$ random events occur at, what is the most likely order that they will occur in? This questions follows ...
2
votes
2answers
63 views

If you roll two six-sided dice, what is the probability that the dice add to 10 or higher?

When answering these sort of questions people mostly resort to diagrams and I'm wondering if there is a way to calculate the probability without going through each outcome, just solely on the given ...
4
votes
1answer
32 views

probability/combinatorics question with marbles

An urn has 20 green out of 50 marbles. Draw all 50 marbles without replacement. Let X = # of green marble runs of any length. Example : GGGGBBBGGBBGBB. . . In the above example, there are 3 runs in ...
0
votes
2answers
27 views

Average Goals Per Game

Okay I am trying to work something out. If for example Team A scored an average of 2.84 goals per game over a period of 95 matches. What is the probability that there next match will be 3 goals or ...
1
vote
1answer
29 views

Finding probability with the help of combinations

$N$ tutors are to be assigned to $s$ students with any student having at most one tutor and similarly any tutor having at most one student. If any tutor is assigned randomly then how can we find the ...
3
votes
0answers
18 views

Suggestions for Constructing a Random Variables from Correlated Observations

Let $\mathcal{X} \neq \phi $ be a finite set. Let $P_{XY_1Y_2}$ be a fixed joint distribution over $\mathcal{X}\times\mathcal{X}\times\mathcal{X}\ $ and that a random sample $(X,Y_1,Y_2 )$ is drawn ...
-2
votes
1answer
45 views

Loaded coin: probability I will never get two heads [on hold]

I'm currently starting to learn probability in an intro course in college and am wondering how to solve this. Given a loaded coin that gives a 60% chance of flipping heads, and 40% chance of tails, ...
0
votes
0answers
10 views

Deriving global probabilities from local dynamics

I am interested in growth dynamics and, in particular, how to derive difference/differential/stochastic equations from local behavior of a system. For concreteness, let's imagine a simple predator/...
1
vote
2answers
52 views

Probability Conjecture

I think there is a flaw in my logic but I'm not sure where it would be. Let HHH denote the event of three coin flips. Let E(HHH) be the expected value of the number of coin flips until HHH. Let E(...
1
vote
1answer
28 views

Scale invariance of uniform distribution over $\mathbb R^2$?

If we make a uniform distribution of points over $\mathbb R^2$ with 1 point on average per unit square. And we zoom far out and make a density plot (give a color to each cell according to how many ...
0
votes
2answers
26 views

Value of c so that $c(2-|x|-|y|)$ is a probability distribution function(see picture)

Hint: Use the formula of volume of pyaramid. My approach: I know that the integral of a pdf from $-\infty to +\infty$ gives you $1$. I tried taking the double integral, but got stuck in as how to ...
0
votes
2answers
633 views

finding probabilty using Methods of Enumeration

A computer retail store has 12 personal computers in stock. A customer wants to purchase three of the computers. Assume that of the 12 computers, 4 are defective. If the computers are selected at ...
1
vote
1answer
38 views

Expected length of a random walk

Let $G = (V,E)$ be a connected graph. Now consider a random walk on $G$, where we pick a random vertex $v_0$ sampled uniformly at random from $V$. Let $v_i \in V$ denote the vertex in the current ...
65
votes
4answers
5k views

Why did my friend lose all his money?

Not sure if this is a question for math.se or stats.se, but here we go: Our MUD (Multi-User-Dungeon, a sort of textbased world of warcraft) has a casino where players can play a simple roulette. My ...
1
vote
1answer
47 views

Expected win of a carnival sharpshooter game

A carnival sharpshooter game charges $\$25$ for $25$ shots at a target. If the shooter hits the bullseye fewer than $5$ times he gets no prize. If the shooter hits the bullseye $5$ times he ...
4
votes
1answer
62 views

Expected win in a selection game

You've got a game where you have two 5x4 boards. In each board there are 20 hidden prizes from 1 to 20 (each board has all 20 prizes). You have 8 moves. In each move you choose a board and a ...
2
votes
1answer
26 views

Expected winnings in betting game [closed]

Suppose you are playing a game where you are betting dollars and if you flip a coin and it is heads, then you win that amount, but if it's tails, you lose that amount. You use the strategy that you ...
0
votes
2answers
51 views

Intuition of the expectation.

Let $(\Omega ,\mathcal F,\mathbb P)$ a probability space. What is the intuition behind the definition $$\mathbb E[X]=\int_\Omega X(\omega) \, \mathrm d \mathbb P(\omega )\text{ ?}$$ I don't see in ...
1
vote
0answers
17 views

Finding Future probability of results within a group of numbers

I apologize in advance if this question, or one similar, has been asked - I couldn't find anything via a quick search. How do I go about finding the probability of any particular number from within ...
1
vote
2answers
742 views

Expected gain or loss in roulette

The questions reads: There are $37$ numbers, from $0$ to $36$. Each number has an equal chance of turning up. Zero is green in color and odd numbers are in black and even numbers are in red. If ...
1
vote
1answer
53 views

Is this betting game profitable?

I'm wondering whether a specific betting game is profitable but I'm not quite sure how to analyse it, some good tips on how to start would be great. Suppose a fair coin is tossed repeatedly. ...
2
votes
1answer
22 views

Understanding the Skorohod-space

I am having a lack of understanding the Skorhodspace considering cadlag processes. A random variable $X$ is measurable mapping between two measure spaces say $(\Omega,\mathcal{F})\mapsto (\tilde{\...
1
vote
1answer
682 views

Find the MOM estimate and the MLE of the Pareto distribution.

The Pareto distribution has been used in economics as a model for a density function with a slowly decaying tail: Assume that $X_0$ > 0 is given and that $X_1, X_2, ..., X_n$ is an i.i.d. sample. ...
1
vote
1answer
20 views

Expected Value when joint density function is given

Let $X_i$ denote the percentage of votes cast in a given election that are for candidate $i$, and suppose $X_1$ and $X_2$ have a joint density function $f_{X_1,X_2}(x,y)= 3(x+y)$ if $x\geq0;y\geq0;0\...
1
vote
0answers
26 views

PDF/CDF of max-min type random variable

For i.i.d. random variables, we may write the CDF of $t=\max(t_1,\cdots,t_N)$ as $$F_t(t)=F_{t_i}(x)^n$$ and the CDF of $x=\min(x_1,\cdots,x_N)$ as $$F_x(x)=1-(1-F_{x_i}(x))^n$$ When we have $X=\...
0
votes
1answer
62 views

Two length 3 straights vs. one length 5 straight. Which is more likely and by how much?

Using a well shuffled standard $52$ card deck, $2$ players (call them A and B) decide to play a game. They draw community (shared) cards (without replacement) until a winner for that hand is ...
8
votes
3answers
5k views

Probability of 20 consecutive success in 100 runs.

Suppose a chess player have a win rate equal 90%, what is the chance to have 20 consecutive wins (successes) playing 100 games? Consider that lose/draw = fail. I've studied basic statistics in ...
0
votes
1answer
502 views

probability - ice cream flavours [on hold]

Of the $50$ ice cream flavours at J.P. Lick’s, $10$ of the ice cream flavours have a vanilla base (as opposed to chocolate or some sort of other flavour base). Of the $50$ ice cream flavours, $15$ ...
-1
votes
1answer
41 views

Loaded die problem.

A die is loaded in such a way that the probability that a 6 is thrown is five times that of any other number, each of them being equally probable. What is the ratio of the probability of obtaining a ...
0
votes
1answer
27 views
+50

Transforming a categorical distribution by repeating trials and taking a plurality

Suppose you have a K-sided, weighted die. This is represented by a categorical distribution. Now, let's say you roll the die N times, and then pick a "winner" by choosing whichever outcome has a ...
1
vote
1answer
22 views

Basic query Related to dependent random variables

$X$ and $Y$ are two dependent random variables. I want to find the following probability $$\Pr(2X<c,4Y>c)$$ wher $c$ is some positive number. In my attempt, I can expand the above probability ...
1
vote
1answer
387 views

Queuing Theory with Poisson Distribution

Suppose customers arrive in a one-server queue according to a Poisson distribution with rate lambda=1 (in hours). Suppose that the service times equal 1/4 hour, 1/2 hour, or one hour each with ...
0
votes
1answer
21 views

Getting the joint function. What am i doing wrong?!?

we have that $f(x_1,x_2)=2(1-x_1)$ if $0≤x_1≤1$, $0≤x_2≤1$. And we have that $Y_1=x_1x_2$ and $y_2=x_1$ And i have to find the joint distribution of $y_1$, $y_2$:(f($y_1,$$y_2$)) and verify if this a ...
-2
votes
2answers
30 views

measure of a set which is a subset of infinitely many subsets of probability measure space [on hold]

Let $B,A_1,A_2,....$ be the subsets of a probability measure space. If $ B \subset \bigcup A_j$, show that $m(B) \le \sum_{j=0}^\infty m(A_j)$. I have no idea as how to approach it. I do have the ...
3
votes
2answers
98 views

Expected number of virus cells

I've found this question in a past programming assignment from a course I'm currently reading. Its statement looks like this : A recent lab accident resulted in the creation of an extremely ...
2
votes
0answers
53 views
+50

Help with conditional expectation of a convolution of exponential random variables

I'm working through this paper, with lots of help from all the great people on this site. Obviously my statistics/probability is a lacking to follow all the mathematical steps. Currently, I'm trying ...
0
votes
0answers
12 views

Help needed related to derivation

I want to find the following probability $$P(z_i\leq min(1,x^{-m})<z_{i+1}, x<x_1|z_i \leq 1, z_{i+1}>1)$$ where $m$ is some value greater than $2$, $z_i$'s are some constants and pdf of $x$ ...
0
votes
1answer
54 views

Poisson distribution with more than one lambda.

An archaeologist has two old pieces of wood and shall decide which piece of wood is the oldest. Radioactivity from the pieces of wood are recorded by a counter. Number of registrations per unit time ...
0
votes
2answers
27 views

Probability - Poisson Arrival Process

Car arrive at a toll booth according to the Poisson process at a rate of 3 arrivals per minute. a) What is the probability that the third car arrives within 3 minutes of the first car? b) Of the ...
2
votes
4answers
67 views

Probability that the second throw of a fair die exceeds the first

A player throws an ordinary die and records the score $A$. The player then throws the die again and again records the score, $B$. if $B>A$ then we set a score for this player. What is the ...
0
votes
0answers
26 views

Upper bound number of self-avoiding walk of length $n$

A self-avoiding walk is a sequence of $n$ neighbor sites on a graph which are all distinct. Let $C_n$ be number of self-avoiding walk of length $n$ in a $d$-dimensional regular lattice. As a ...
0
votes
0answers
36 views

A game of blackjack with guaranteed 50 50 win loss

Suppose you are playing 2 hands of blackjack at the same time and the dealer guarantees if you lose hand A they will pay whatever you bet for hand B but if you win hand A you automatically lose hand B....
0
votes
1answer
47 views

What is the expectation of $X$ given $XY > \alpha$

Suppose $X$ and $Y$ are non-negative independent random variables. Then how can I evaluate $\mathbb E[\ X\ |\ XY > \alpha\ ]$ for some $\alpha > 0$? If I know the precise distributions of both ...