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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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Probability and exit polls

I have a very simple probability question that I for some reason just can not solve. Question: Consider an election with two candidates, Candidate A and Candidate B. Every voter is invited to participate in an exit poll, where they are asked whom…
Soren123
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Effects of condensing a random variable to only 2 possible values

$X$ is a random variable, which is not constant. $E[X]=0$. $E[X^4] \leq 2(E[X^2])^2$. Let $Y$ be given by: $P(Y=E[X|X \geq 0]) = P(X \geq 0)$ and $P(Y=E[X|X \lt 0]) = P(X \lt 0)$. Do we necessarily have $E[Y^4] \leq 2(E[Y^2])^2$?
Mark
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Can a sample space consist of only the empty set?

On the axioms of probability we have that on the one hand the probability of the sample space $\Omega$ to happen is 1; in other words: $$ \mathbb{P}(\Omega) = 1$$ But on the other hand we also have that for any probability space the probability of…
McGuire
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Modified two child problem. Find the probability that both are girls, given that at least one is a girl born in March.

A family has two children. Assume that birth month is independent of gender, with boys and girls equally likely and all months equally likely, and assume that the elder child’s characteristics are independent of the younger child’s…
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60 balls in a bag

I have a question, but I also have the solution. My problem is that I don't understand the solution! Question: There are 10 red, 20 blue, 30 green balls in a bag. You keep removing balls at random. What is the probability that when you take the last…
Bazman
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probability of picking a specific card from a deck

Question: What is the probability you draw Jack of Hearts in a hand of $5$ cards? Assume you have a deck with with $52$ cards ($4$ suits of $13$ cards: numbers $1\ldots 9$, and faces J, Q, K). My way of thinking is the…
JuneK
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Probability of Heads in a coin

I was wondering, if you flip a fair coin $5$ times, whether you can calculate the probability of getting at least one head is calculated like this: You can do the complement of getting at least one head which is TTTTT: $\dfrac1{2^5}…
Xabi
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Probability question using fixed steps

I start life at $0$, I aim to make it to $1$. I can take steps of $\dfrac{1}{2^k}, k>0$, and do so with probability $\dfrac{1}{2^k}$. What is the expected number of steps to reach $1$ or beyond. What is the probability I will land on…
JMP
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Coin toss problem, get exactly 2 heads in 5 tosses

Suppose we toss a fair coin until we get exactly 2 heads. What is the probability that exactly 5 tosses are required? My try: We have to make sure that the first 4 tosses does not have 2 heads and the last toss must be a head. That is, the…
spatially
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When to consider the ordering for probability.

A rather fundamental concept which I somewhat failed to grasp and now is jeopardising my further understanding/solving of probability problems.. In the case of this question, where we are to find the probability, that the minimum of two throws of a…
Jon Gan
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Bingo probability of a tie with 20 players

Assume "standard" bingo (75 numbers) with the columns ranging the following inclusive "semi-random" values B: 1 to 15, I: 16 to 30, N: 31 to 45, G: 46 to 60, O: 61 to 75. By semi-random I mean restricted to a small range (15 at a time). There is a…
user263122
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How to compute an expected value in shorter ways (when taking all possibilities into account isn't plausible.)

There is this question on which I have been spending a lot of time, trying to understand how to compute an expected value in a comprehensive way, as sorting out all the possibilities doesn't seem like that right thing to do, nor does it even seem…
Meitar
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An Average of Probabilities

This is an open ended question in that the desired end result is not well posed. Still, it may be of some interest. Suppose you have a number of teams which play against each other in two team competitions (all pairings occur with equal likehood,…
lulu
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off by 1 lottery probability

A lottery, where 6 balls out of 50 are drawn randomly without replacement, allows players of the lottery to be off by at most 1 for each number on their lottery ticket. Additional rules of the lottery are as follows: The balls are numbered 1 thru…
David
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Frequency from probability

Assume an event has a probability $p=1/100$ of happening, per trial. Here are three statements that I believe are true: On average, the event is witnessed in a one-hundredth of the the trials. The average number of trials between consecutive events…
user41837
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