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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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How far to look before line-of-sight will intersect a star

I was told this sort-of riddle by someone, having to do with the proof for the finite age of the universe, and I'm not sure how to approach the answer. Assuming that the entire universe is uniformly filled with sun-like stars (let the sun-radius be…
jake
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$10$ people and $2$ of them are traitors

Let's suppose you are playing a game similiar to “Among Us”. There are $10$ players and $2$ of them are impostor/traitors. Normally, they would kill people secretly stab people, convince, manipulate, lie and etc. to win the game but lets spice…
Yağız Alp Ersoy
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Probability of forming triangle from breaking a stick

Given a stick and break it randomly at two places, what is the probability that you can form a triangle from the pieces? Here is my attempt and the answer does not match, so I am confused what went wrong with this argument. I first denote the two…
Xiaohuolong
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How Can the Birthday Problem be solved directly

How would one go about solving a variant of the birthday problem given below "What is the probability of at least two people having the same birthday in a group of 23" I know the answer is just above 0.5 but I am interested in how it is solved when…
Obi Ike-Nwosu
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Poisson CDF as lower bound to binomial CDF

Consider two random variables $X \sim \operatorname{Binom}[(n,p)]$ and $Y\sim\operatorname{Poisson}[(\lambda)]$, where $\lambda = n p $. Let their respective CDFs be $F_X(k)$ and $F_Y(k)$, then I would like to show that $$ F_Y(k) \leq F_X(k) $$ but…
okintheory
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Given a deck of cards, what are the odds of consecutively drawing higher cards for a given number of draws?

Lets say you're trying to draw n cards, each higher than the last. How likely are you to succeed in consecutively drawing higher for a given starting number & number of iterations? Somebody said to add my thoughts to the question! We've had a lot…
Karrsen B
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Probability: Drawing two marbles simultaneously from the bag

This is a 9. grade elementary school quiz problem. There is a bag with 4 marbles. Two of them are yellow and the other two are green. You blindly pick two marbles at once. What is the probability that you get two yellow marbles? I would say the…
Matic Potocnik
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Find the probability that no more than three attempts will be required to open the lock

Of the five keys, one is suitable for the lock. The key that did not fit when trying to open the lock is put aside. We need to find the probability that no more than three attempts will be required to open the lock. I tried to use the…
Egor
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Probability you run out of white balls first?

I saw this question online (interview brainteaser prep), and can't get my head around it. You have $r$ red balls, $w$ white balls in a bag. If you keep drawing balls out of the bag until the bag only contains balls of a single color (i.e you…
user1887919
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Probability of drawing a white ball given optimal distribution of balls

Suppose you have 10 white balls, 10 black balls, and 2 baskets. You may place some of the balls into one basket and the remaining balls into the other basket however you wish. After you are done, your friend Janelle will flip a fair coin to select…
Roland Fannoh
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Determine the probability that the group will score more than 80 points

A group of $20$ students take the exam. The probability that the student will receive a grade of $2$ - $0.1$, grade $3$ - $0.3$, grade $4$ - $0.4$, grade $5$ - $0.2$. Determine the probability that the group will score more than $80$ points. Can you…
Mario Grazione
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Run of $N$ successes before run of $k$ failures

What is the probability that a run of $N$ consecutive successes will occur before a run of $k$ consecutive failures when each trial has a probability $p$ of success and $q=1-p$ of failure?
Jean-Pierre
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What is the probability that you never lose this hypothetical dice game?

You have a four sided die numbered 1-4 and are playing a game. On the first round, you roll the die once. If you get a 1 you lose the die. If you get a 2 you keep the die. If you get a 3 or 4 you get another, identical die. On the second round you…
user737519
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Difficult probability question

Four French teams make it to the final eight of the Champions League. The draw for the round is made at random. What is the probability that exactly one pairing has two french teams? ... At first, I recognised that there could only either be 0…
Mr Field
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If $\mathbb E[e^{\xi X}]=e^{\frac{\xi^2}{2}}$ for all $\xi >0$ does $X\sim \mathcal N(0,1)$?

I know that if $$\mathbb E[e^{\xi X}]=e^{\frac{\xi^2}{2}}$$ for all $\xi\in\mathbb R$, then $X\sim \mathcal N(0,1)$. Now, if $$\mathbb E[e^{\xi X}]=e^{\frac{\xi^2}{2}}$$ for all $\xi >0$ does $X\sim \mathcal N(0,1)$ as well ? I really can't find a…
John
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