# 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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### 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 ...
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### Probabilistic Method/Model for Traffic Flow

Context: Given a network system or a traffic system with some value related to the system. Question: Which probabilistic methods, model, distributions are used frequently to predict a event (for ...
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### Conditional statestic

I have this exercise. A batch of 500 containers for frozen orange juice contains ten that are defective. Two are selected, at random, without replacement from the batch. (a) What is the ...
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### I am stucked in some of this question about sample space and probability

What is the size of the sample space for the following scenario: Roll $3$ six-sided dice, and discard the highest roll In this question I know that sample space is all possible outcomes so the ...
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### How long does it take a person with this “cheating” data-gathering strategy to achieve a desired result?

I have a perfectly fair coin, and my goal is to prove that it is unfair with a confidence level of 95%. In order to accomplish this, I will cheat. Whenever I fail to have enough evidence, I will ...
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### 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 ...
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### Is there a way to maximize this probability by taking the derivative of the cumulative normal distribution function?

I'm self-studying Brownian motion and encountered the following problem. I understand the author's solution, and it is clear why maximizing the right-hand side of the inequality provides such $t$ ...
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### Probability Question - Pls help

A salesperson visits $k$ clients each day. The salesperson makes one and exactly one sale each day. The probability that the salesperson makes a sale to the $j$th client on a given day is $p_j$, ...
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### Comparing log functions of CDFs and PDFs (related to order statistics) with non-log functions of the same

Let $f$ and $F$ denote the respective pdf and cdf of a probability distribution on $\mathbb{R}$. Take any natural $n\geq3$ and any real $a$ and $c$ such that $a\leq c$, and $\rho\geq0$. We want to ...
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### Odds of 10 thrown dice landing all the same

What are the odds of throwing $10$ six sided dice and landing all the same number. Also, how many throws would I need to do to achieve a $100$ percent success of this happening. Is this even possible ...
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### Predict the daily usage of Bandwidth of a Network

Context: I want to predict the daily usage of bandwidth of a network (consists a number of users) based on previous use . For example, I want to predict the amount of bandwidth during 8 pm to 9pm ...
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### How to find a mean probability

A speaks truth in 75 cases just of hundred while B speaks truth in 80 cases out of hundred.Find the number of cases where they are likely to contradict. I did try working it out.So out of 200 ...
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### Detailed explanation needed for basic query regarding expectation

I need to find the expectation of following random variable $$g=[\log_2(\frac{1+x}{1+y})]^+$$ where $[x]^+=max(x,0)$ and both $x,y$ variables depend on variable $z$. I know the conditional pdf's and ...
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### What are the odds of flipping a coin 100 times and seeing HHHHT? [on hold]

What are the odds of flipping a coin 100 times and seeing exactly four consecutive heads? Any more than four heads in a row, such as "HHHHH" would not be considered a string of four consecutive heads. ...
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### Conditional probability using set notation [on hold]

Got this wrong on a quiz and i don't have the answers. Need to figure this out for a test coming up. \begin{align} P(A) &= 0.75 \\ P(B\mid A) &= 0.9 \\ P(B\mid A^c) &= 0.8 \\ P(C\mid A\...
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### When to stop pumping up balloons?

Yesterday I acted as a volunteer in a psychology/neurology experiment where one of the trials consisted of playing a computer game in which you had to click the mouse to pump up a balloon. For each ...