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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2answers
26 views

Proof Question- Need Help [on hold]

Show that if $P(A|E) \geq P(B|E)$ and $P(A|E^c) \geq P(B|E^c)$, then $P(A) \geq P(B)$. I am reviewing for test, and I came across this problem in the textbook. I need help with this question.
0
votes
1answer
15 views

Soft: Interpretation of a periodic event on circle group

Recently I've been exploring probability measures on topological groups, derived from the (essentially) unique Haar measure defined thereon. I had begun to focus on the example of the circle group ...
0
votes
0answers
25 views

probability expression deriving

A deck of n=10 cards is numbered from 1 to 10.The cards are shuffled and laid down from left to right, face up. Order each of the five successive pairs of cards. Each of these five pairs determines a ...
2
votes
2answers
88 views

Hat Matching Problem Expectation

I have an interesting problem in the context of the hat matching problem: There are n people with hats at a party. Each person randomly grabs a hat. A match occurs if a person gets his own hat. I'd ...
1
vote
1answer
27 views

Stopped sigma-algebra for a counting process

let $(\Omega, \mathcal{A}, P)$ be a probability space and $(N_t)_{t \geq 0}$ a right-continuous counting process with jumps of size 1, $N_0 = 0$ and canonical filtration $\mathcal{F}_t := \sigma( N_u ...
-2
votes
1answer
30 views

Question I couldn't identify to solve this distribution [on hold]

A couple decides to have 3 children.If none of them is a girl,they will try again,and if they still don't get a girl,they will try again and continues so on.If X is the number of children,the couple ...
-1
votes
0answers
23 views

Brownian motion-Holder [on hold]

there exists a positive constant $c$, such that almost surely, for h small enough , for all $0< t < 1- h$ \begin{align} |B(t+h)-B(t)| < c\sqrt{h\log(1/h)} \end{align} As a result ...
0
votes
1answer
13 views

Related to chi-squared functions

I'm finding difficulty in finding what type of function it is in continuous distributions in probability.Mainly how can i identify whether a function is chi-squared or not?
1
vote
4answers
85 views

If a monkey types each letter of alphabet exactly once, what is the probability of the word “Hamlet” appearing?

A monkey types each of the 26 letters of the alphabet exactly once (the order is random). What is the probability that the word Hamlet appears somewhere in the string of letters? Progress So far I ...
1
vote
2answers
32 views

Continuous and Discrete random variable distribution function

I have a very basic question in probability. It pertains to the difference between a continuous random variable distribution function and a discrete one. This question has confused me many times. ...
0
votes
1answer
28 views

Approximations of hitting times of biased random walks

Let $X, X_i$ be iid with mean $\mu$ and variance $\sigma^2$ and $h>0$ be the stopping position. Let $S_n=X_1+...+X_n$ and $T$ be the number of steps it takes to walk beyond h. I need to find the ...
1
vote
1answer
35 views

Book to self-learn probability

I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one ...
1
vote
0answers
27 views

Polya urn scheme probability calculation

Consider an urn with $b$ black and $r$ red balls. In each step we randomly choose a ball. Then we put it back in and put $c$ balls of the same color in the urn. Let us denote $B_m$ as the event that ...
2
votes
1answer
27 views

Coin-tossing games

Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you ...
-1
votes
1answer
8 views

Probability of choosing from population with 10% trait

In a large city, 10% of the population has green eyes i) What is the probability that exactly two of a group of 20 randomly chosen people have green eyes? ii) What is the probability that more than ...
0
votes
2answers
17 views

one ball is drawn at random from each box, what is the probability that both the balls are of the same colour?

Boxes 1 and 2 contain 4 white, 3 red and 3 blue balls; and 5 white, 4 red and 3 blue balls respectively. If one ball is drawn at random from each box, what is the probability that both the balls are ...
0
votes
2answers
62 views

Best E-books and online-resources for Probability and its applications(especially games of chance)

I am very much interested in studying games of chance and the probabilities related to our daily life instances but I need an online resource or some e-book to study them. I am a self-learner. Can ...
0
votes
0answers
33 views

deriving probability expression [on hold]

A deck of $n = 10$ cards is numbered from $1$ to $10$.The cards are shuffled and laid down from left to right, face up. Order each of the five successive pairs of cards. Each of these five pairs ...
0
votes
0answers
12 views

what does the set of nonterminating fractional expansions of the interval (0,1] look like?

Suppose I define $\Omega$=(0,1] and $\omega$ represents a single fractional expansion in the interval. If $B$ = the set of all possible outcomes that are not terminating (not finite) fractional ...
1
vote
1answer
36 views

Probability: basic question and concept

I have always been struggling with the problem, in particular, I usually have great difficulty in differenting when should I multiply n! to take care of the ordering, and when should I not do so. For ...
0
votes
1answer
11 views

how to show the probability of no occurrences of a single digit in a fractional expansion is a simple formula?

Say I have a binary string of length 1. What is the probability I never see a 0? My binary string can only be a 0 or 1. So obviously the probability I never see a 0 is 1/2. If instead I have a base ...
0
votes
0answers
29 views

Calculating Expected Value when terms involve Max and Summations

Suppose $A= \sum_{k=1}^{n/2}X_i$ and $B=\sum_{k=n/2+1}^{n}X_i$ $X_i$ is a random variable which takes on values 5,6,7 and 8 with equal probability. What is expected value of ...
0
votes
1answer
34 views

Divergence of $\sum_{m=0}^{\infty}\xi_{m}2^{m+1}$, where $\xi_{m}\sim N(0,1)$?

This is homework, so no answers please $\xi_{m}\sim N(0,1)$ and independent of each other. I think the following will diverge $\sum_{m=0}^{\infty}\xi_{m}2^{m+1}$, where $\xi_{m}\sim N(0,1)$. One ...
1
vote
2answers
20 views

Permutations and Sample Spaces

Suppose 3 cars can either turn left $(L)$, turn right $(R)$, or go straight $(S)$. I need to find the sample space for all the possibilities but I am not sure how to do that. I know that for 3 cars ...
0
votes
3answers
38 views

rolling dice do not understand this problem know it is going to be easy once I get it

If a pair of dice are rolled, what is the probability that the sum is less than 7 or at least one of the die rolled is a 2? I have tried to work this type of problem out and I just can't get an ...
1
vote
2answers
47 views

Probability that 20 sided die beats 12 sided die with reroll

Alice rolls a 12 sided die (the faces labeled 1 through 12) and Bob rolls a 20 sided die (the faces labeled 1 through 20). After seeing their roll (but not the other person's roll), each person can ...
0
votes
0answers
34 views

balls in bins — waiting time until $k$ bins are occupied

Consider the classic balls in bins problem: we throw balls one by one into $n$ bins independently and uniformly. Define $\tau(k)$ for $1 \le k \le n$ to be the number of balls we have thrown until $k$ ...
0
votes
1answer
30 views

Under what assumptions can one compute conditional probability as $p(x)/p(y)$?

Conditional probability is often introduced in the following way: Consider a normal, fair 6-sided die. If you toss it then the probability $p(x=2)=1/6$. Now given that we already observed that the ...
0
votes
1answer
12 views

Geometric distribution: the probability of winning in fewer than 3 attempts

I have a seemingly simple problem but I can't find the one solution listed among the possible solutions: We have a heads or tails game with probability to win equals to $0.2$ (heads) at each play. ...
0
votes
2answers
20 views

convergence in distriubtion of $(\max_{1\leq k\leq n} X_k)/ln(n)$ where $X_k\sim \text{Exp}(1)$.

The problem is: Let $X_k$'s be i.i.d. $\text{Exp}(1)$ r.v.'s. define: $$\xi_n = max_{1\leq k\leq n} X_k$$ $$\eta_n = \xi_n/ln(n)$$. The question is what is the limit of $\eta_n$ as $n\to \infty$? ...
3
votes
1answer
22 views

Probability that an urn contains 3 balls after 20 draws - without replacement -

Looks to me as a hard problem: Let's say we have two urns $A$ and $B$. Initially, $A$ is empty and $B$ has $100$ balls. At each draw, we randomnly choose a ball with equal chances (among the whole ...
-2
votes
0answers
33 views

Minimise the expected value [on hold]

Given an array A that contains n integers, namely $A[1], A[2], ..., A[n]$. A single action consists of performing one of two following operations: ...
1
vote
0answers
32 views

Stochastically continuous but a.s. discontiuous process

This is a homework question so no answers please The problem is: Find a process $X_{t}$ s.t. $\forall t_{0}\geq 0$ and $\varepsilon>0$ we have $lim_{n\to ...
0
votes
0answers
24 views

Probability distribution of a function of an Erlang random variable

Suppose $S_n$ is an Erlang random variable with parameter $\lambda$ and $n$. Let $S_0 = 0, N = \max_{n\geq 0}\{S_n \leq t\}$. What is the distribution of $N$? Here's what I have: $N$ is a discrete ...
0
votes
1answer
18 views

Lifetime of Light Bulbs - Probability Question

This is the question that I have, so I solved the first two parts very easily. The first part (i) Then the part (ii) Now, I dont know how to do the final part of the question (it is too ...
0
votes
2answers
18 views

Probability of selecting at least one from each group probability

A team of 5 managers is to be selected from a group of 10 managers - 5 from company A, 3 from company B, and 2 from company C. In how many ways can this be done if the team must contain at least one ...
3
votes
5answers
110 views

Probability of a 75% freethrow shooter making at least 5 shots in a row out of 10.

What is the probability that a 75% free throw shooter, given the assumptions listed below, can make at least $5$ in a row of $10$ shots? So in effect he must make $5$, $6$, $7$, $8$, $9$, or all $10$ ...
0
votes
1answer
23 views

Applications of random walks

I am searching for a clear and interesting exposition of an application of random walks to some physics topics accessible to advanced high school students.
0
votes
1answer
29 views

Probability of 50% success chance after 10 trials?

Sorry this may be a simple question but i can't figure out the answer to this. If I for example, flip a coin 10 times. What is the percentage chance of getting just 1 Heads? Is it always 50% in the ...
2
votes
1answer
23 views

The math behind generating Dungeons & Dragons ability scores: roll 4d6, toss lowest

D&D 5th ed. gives the following instructions for determining your “ability scores.” Roll four 6-sided dice and record the total of the highest three dice If I repeat the ...
0
votes
0answers
6 views

Methods for Uncorrelating data - Comparison

I see that both PCA and Cholesky Decomposition could be used for uncorrelating correlated data. When should one be used? What are the assumptions made by each model. When do the methods fail? Are ...
0
votes
0answers
41 views

Brownian motion - Holder continuity

Let $B$ stand for a brownian motion on a finite interval $[0,1]$. If i am not wrong, i think that there exists a positive constant $c$, such that almost surely, for h small enough , for all $0< t ...
1
vote
1answer
26 views

Probability Question - Number of boxes one should look at

Will someone help me understand how to solve the following ? Jenny has 10 boxes all containing clothes. She is looking for her white pants, but has the following problem: while searching, she can ...
1
vote
1answer
27 views

Probability of words

The question is as follows: A word of $6$ letters is formed from a set of $16$ different letters of English alphabet (with replacement). Find out the probability that exactly two letters are ...
0
votes
2answers
34 views

How to find the probability of a score from multiple dice with varying sides

I'm trying to find a general method for working out the probability of a score from rolling several dice with varying sides. For example, the probability of getting a result of 12 when rolling two ...
3
votes
1answer
40 views

Applying Combinatorics to College Applications

From a list of 4,000 colleges, I have a list of 50 colleges. From that list of 50 colleges, I now plan to choose 15 colleges to apply to. Each of the 50 colleges has a scale value (how well the ...
2
votes
0answers
50 views

Quibble with Dawkins's reasoning on the watch-stopping probability on a psychic audience

In Unweaving the Rainbow (page 150) Richard Dawkins mentions the following (famous) reasoning on why it's almost certain that a psychic with a big audience will accurately predict/command rare events ...
0
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0answers
16 views

Extension of martingale representation theorem.

It seems that the proof I am reading of the Martingale Representation Theorem, "A square integrable RCLL martingale which is adapted to the augmented filtration of a Brownian Motion must be an Ito ...
0
votes
1answer
14 views

Probability the number Zero appears in a Canadian Postal code (of format x#x #x#), where x denotes a letter

first post. Doing some basic probability, and although I got an answer to the question, something's telling me in the back of my mind that I did it incorrectly. The question is: What is the ...
2
votes
1answer
33 views

Square integrable stochastic process

Suppose that for a stochastic process we have \begin{align} \mathbb{E}\left[\int_{0}^{T}X^{2}(t)dt \right]<\infty \end{align} where $T<\infty$. Does it holds that $|X(t)|<M$, where $M$ ...