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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Multiple-choice question about the probability of a random answer to itself being correct

I found this math "problem" on the internet, and I'm wondering if it has an answer: Question: If you choose an answer to this question at random, what is the probability that you will be correct? a. $25\%$ b. $50\%$ c. $0\%$ d. $25\%$ Does this…
user11088
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In Russian roulette, is it best to go first?

Assume that we are playing a game of Russian roulette (6 chambers) and that there is no shuffling after the shot is fired. I was wondering if you have an advantage in going first? If so, how big of an advantage? I was just debating this with…
nikkita
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Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?

Of course, we've all heard the colloquialism "If a bunch of monkeys pound on a typewriter, eventually one of them will write Hamlet." I have a (not very mathematically intelligent) friend who presented it as if it were a mathematical fact, which got…
Jason
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Do men or women have more brothers?

Do men or women have more brothers? I think women have more as no man can be his own brother. But how one can prove it rigorously? I am going to suggest some reasonable background assumptions: There are a large number of individuals, of whom half…
layman
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Counterintuitive examples in probability

I want to teach a short course in probability and I am looking for some counter-intuitive examples in probability. I am mainly interested in the problems whose results seem to be obviously false while they are not. I already found some things. For…
191
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Can a coin with an unknown bias be treated as fair?

This morning, I wanted to flip a coin to make a decision but only had an SD card: Given that I don't know the bias of this SD card, would flipping it be considered a "fair toss"? I thought if I'm just as likely to assign an outcome to one side as…
Andrew Cheong
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Taking Seats on a Plane

This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless Imagine there are a 100 people in line to board a plane that seats 100. The first person in…
crasic
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Is the product of two Gaussian random variables also a Gaussian?

Say I have $X \sim \mathcal N(a, b)$ and $Y\sim \mathcal N(c, d)$. Is $XY$ also normally distributed? Is the answer any different if we know that $X$ and $Y$ are independent?
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Monty hall problem extended.

I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$)…
Shaurya Gupta
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What is the best book to learn probability?

Question is quite straight... I'm not very good in this subject but need to understand at a good level.
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Sum of random decreasing numbers between 0 and 1: does it converge??

Let's define a sequence of numbers between 0 and 1. The first term, $r_1$ will be chosen uniformly randomly from $(0, 1)$, but now we iterate this process choosing $r_2$ from $(0, r_1)$, and so on, so $r_3\in(0, r_2)$, $r_4\in(0, r_3)$... The set of…
148
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What's 4 times more likely than 80%?

There's an 80% probability of a certain outcome, we get some new information that means that outcome is 4 times more likely to occur. What's the new probability as a percentage and how do you work it out? As I remember it the question was posed like…
Jim
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Intuition behind Conditional Expectation

I'm struggling with the concept of conditional expectation. First of all, if you have a link to any explanation that goes beyond showing that it is a generalization of elementary intuitive concepts, please let me know. Let me get more specific. Let…
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Expected time to roll all $1$ through $6$ on a die

What is the average number of times it would it take to roll a fair $6$-sided die and get all numbers on the die? The order in which the numbers appear does not matter. I had this questions explained to me by a professor (not math professor), but…
eternalmatt
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What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges?

My friend gave me this puzzle: What is the probability that a point chosen at random from the interior of an equilateral triangle is closer to the center than any of its edges? I tried to draw the picture and I drew a smaller (concentric)…
terrace
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