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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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Coin tossing - what's more probable?

I am solving the following probability exercise. The solution I have found is very counter intuitive and I feel It is wrong, but I can't seem to understand why. A fair coin is tossed twice, you have to decide wheter it is more likely that two…
qcc101
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Probabilities of one-off events

I am teaching 15 year olds basic probability. I am teaching them "experimental probabilities" (eg the probability that it will rain on a given day in August is 0.15) vs "theoretical probabilities" (eg the probability of throwing 3 Heads in a row is…
Peter Webb
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How do we explain the "Bad Luck" in probability?

Say, in the game of Pokemon Go, the probability of catching a shiny Pokemon is $\frac{1}{450} \approx 0.22222\%$. Some players consider that "lucky". And by the Law of Large Numbers, we can say, if we catch 450 Pokemon per day, then over the long…
nonopolarity
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Expectation of $X$log$(X)$ when $X$ is Poisson random variable

I am trying to compute $\mathbb{E}[X\mathrm{log}(X)]$ where $X$ is a Poisson random variable with mean $\lambda$, so $Pr(X=x) = \frac{e^{-\lambda}\lambda^x}{x!}$. My usual approach to computing $\mathbb{E}[f(X)]$ is to take the Taylor series of $f$…
David Pfau
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The day I finally get the second sunny day I leave. What is the probability that I stayed exactly one week?

Each day in Iceland, it rains with a probability p=0.8. Denote X the number of days I stay until I've had 2 sunny days in my holidays. What is the p.m.f. of X? The day I finally get the second sunny day I leave. What is the probability that I stayed…
James Anderson
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During certain sequences of coin flips, why does HHHT have a greater chance than HHHH?

I was reading an article, They were comparing sequences of coin flips. They said: "HHHT and HHHH are equal only if flipping an unbiased coin exactly four times or infinitely many times. For values in between these two extremes, probabilities will…
Terry
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Throwing a $6$ in the $n+1$th throw

A fair die is thrown repeatedly until a six appears for the first time. Let $A_n$ be the event that a six appears for the first time on the $n$-th throw. Let $B_r$ be the event that a five appears $r$ times before a six appears for the first…
popping900
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Probability, dependent Events

I am trying to understand some of the tasks and would be happy if someone could check my solution and possibly point out any mistakes. In advance, I am not asking for a solution, because I would like to work it out by myself. The purpose of this…
H4x9r
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Sum of Random Variables...

Imagine we repeat the following loop some thousands of times: $$ \begin{align} & \text{array} = []\\ & \text{for n} = 1: 10 000 \\ & k = 0 \\ & \text{while unifrnd}(0,1) < 0.3 \\ & k = k + 1 \\ & \text{end} \\ & \text{if k} \neq 0 \\ & \text{array}…
user66280
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Calculation of Confidence Interval

We randomly choose 1000 people and run a survey on whether they prefer Apples or Berries. The results are $71\%$ for Apples and $29\%$ for Berries. We want to calculate the Margin of error of the poll, with confidence level $90\%$. My attempt, as I…
Samuel
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Probability for dummies

I am the least mathematical person around, so apologies if this question is really dumb, but I'm trying to improve! I've been reading loads of examples everywhere but I'm having a hard time applying the logic/rules of probability to new…
Lalaca
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Probability of a submatrix with all 1s

I'm not an expert and while reading an article on grid coloring these two questions came to my mind: Given a $n \times n$ matrix randomly filled with values in $\{0,1\}$ ( $P(a_{ij} = 1) = 1/2$), what is the probability that it contains at least…
Vor
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Intuitive Understanding of Independence of 3 Events

I understand what it means to say that an even E is independent of an event F, it means that knowing that F has occurred does not change the probability that E will occur. Algebraically, it implies: $$P(E) = P\left(E \mid F\right) …
cuppajoeman
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Recovering random variable from its moments

The problem is: can you recover a distribution of random variable if you know all its moments? My first guess was to use moment-generating function (MGF). It is known that if two random variables have the same MGF, then they have equal…
esokolov
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What are the chances of rain on particular days

I study maths as a hobby and am on to elementary theory of probability. I have come across this problem: Find the probability of events A, B and C given it rained on exactly 2 days last week. A: it rained Monday and Tuesday B: it rained on 2…
Steblo
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