# Tagged Questions

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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### Predicting certain independent events (each have a known probability)

Consider 15 independent events, each of these events can have three states (for example they can be 1, 2 or 3). Now for example in the event one there is 20% chance of getting 1, 45% of getting 2 ...
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### How exactly is the St Petersburg Paradox giving bounded payoff in average-of-N-trials?

I understand why the expected value of the St Petersburg Paradox is algebraically infinite, but intuition tells me that in practice any given round of the game will not go on multiplying the pot for ...
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### Find out a probability from a set [closed]

I have set A = [ 1 0 0 1 0]; in this set, the number of 1's is two and the number of 0's is three. Question: How to calculate probability of randomly selecting a 1 from set A? (without replacement of ...
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### Probability problem

I created this problem based on the following probability riddle here. You're a king, and you were given two groups of people, and a certain information about them. First group has 2 people. One of ...
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### How many days will it take me to earn a certain sum of money (given a certain probability)?

Suppose I want to earn $7000$. How many days will it take me to earn it, if there is an $80\%$ chance I will make $500$ on a particular day and a $20\%$ chance I will lose $1500$ on the same day? My ...
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### What is the expected number of triangles contained in this graph?

I can't seem to understand this question and I really don't know where to start. Could someone please give an explanation as to how to go about answering this? A simple graph is formed randomly on ...
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### Ticket lottery question

A hundred tickets are marked $1,2,3,...100$, and they are arranged at random. Four tickets are picked from these and given to four persons A,B,C,D. What is the probability that A gets the ticket ...
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### Probability: What is the condition for 3 random variables to be independent [closed]

I know that the condition for 3 events (A, B, C) to be independent is: $\mathbb{P}(ABC) = \mathbb{P}(A)\mathbb{P}(B)\mathbb{P}(C)$ But is it the condition the same for random variables X, Y, Z? For ...
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### Logistic regression for football results - Estimating coefficient through maximum likelihood

Consider two football teams $V$ and $L$ with strengths $W_V$ and $W_L$, respectively. Let's assume that the draw probability $\mathbb{P}(Draw)$ is known. Then this model is supposed to give estimates ...
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### Distribution of number of players who draw, with n independent games of chess

In a chess tournament, n games are being played, independently. Each game ends in a win for one player with probability 0.4 and ends in a draw (tie) with probability 0.6. Find the PMFs of the number ...
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### Probability: Prove that events are independent

I'm self-learning probability and struggle on the following task: If $A$ and $B$ are independent events, prove that $A \cup B$ and $A \cap B$ are also independent. This is one of those cases where ...
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### Conditional negative binomial

An urn contains white and black balls with $p_w=p$ and $p_b=1−p$. Some extractions with replacement are made. $X_a$ is the random variable representing the number of extractions made in order to get ...
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### How does probability change the more times you perform a procedure?

I have a question based on fair coins. Every round, two coins are flipped. If both are heads, we say "Success" and end the experiment. What is the probability of saying "Success" in any round i? ...
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### Picking pairs of socks from a drawer.

There are $n$ socks in a drawer, of $m$ different colours. Initially, the probability of picking a sock of colour $c_i$ at random is $\mathbb{P}(c_i) \cdot 2r$ socks are picked at random, without ...
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### Multinomial distribution and conditional probability

An urn contains $w$ white, $b$ black and $r$ red balls. $n$ extractions with replacement are made. $X_w$, $X_b$ and $X_r$ are the random variables representing the number of white, black and red balls ...
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### The Executioner Conundrum [closed]

You are a military executioner tasked with eliminating some of the most dangerous criminals on Earth. You are handed 100 such criminals for immediate termination. However, just as you are about to ...
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### What are the odds that truck a arrives before truck b? [closed]

given truck a arrives at a random time between 9am and 11am, and truck b arrives at a random time between 10am and 12pm (noon). what are the odds that truck a arrives before truck b
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### Expected numbers of boys in a family

Given $2000$ families with $4$ children in each family and suppose each sex is equally likely, what is the expected numbers of families having at least one boy? Hint: One friend tell me that $X$ ...
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### Understanding the solution of finding the number of red balls drawn before the first black ball is chosen

Question: An urn contains $n + m$ balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let $X$ be the number of red balls removed ...
4 balls are thrown randomly into two baskets (Basket A, Basket B), what is the probability that 2 or more balls will be in Basket A, I'm not sure im correct but $\Omega = 5$. because there are 5 ...