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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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A die is rolled until a 6 comes up. Should the sample space of this experiment contain the set of all infinite sequences which do not contain a 6?

Is there a standard way to view this? The problem is, In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment? My first instinct was to say that it was the set…
crf
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Why wrong or unacceptable to write Pipes on their own, without any probability?

I see mixed messages. heropup commented $(C \mid B) \mid (A \mid B)$, but Michael Hardy chided that "$\color{Red}{\text{There's no such thing as A∣B.}}$ When one writes Pr(A∣B), one is NOT writing about the probability of something that's called…
user53259
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Language and probability - "given that"

In the book "An Undergraduate Introduction to Financial Mathematics" there is a following simple problem: "Suppose cards will be drawn without replacement from a standard 52-card deck. What is the probability that the fourth card drawn will be an…
James Ramson
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Joint to marginal distribution does not make sense

Let the joint distribution of $X$ and $Y$ be $$ f_{X,Y}(x,y) = \begin{cases} cxe^{-2y} &0\leq x\leq 1, y> 0 \\ c(2-x)e^{-2y} &1\leq x\leq 2, y> 0 \\ 0 &\mathrm{else} \end{cases} $$ Find the value of $c$. $$\underbrace{\int _1^2\int_0^\infty c(2-x)…
Illuminate
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Are two independent events $A$ and $B$ also conditionally independent given the event $C$?

If we know that two events $A$ and $B$ are independent, can we say that $A$ and $B$ are also conditionally independent given an arbitrary event $C$? $$P(A\cap B) = P(A)P(B) \overset{?}{\Rightarrow} P(A\cap B|C) = P(A|C)P(B|C)$$
Parna
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Help with conditional probability?

I've got to show that: $$\mathbb{P} (A | A \cap B) = \frac{ \mathbb{P}(A)}{ \mathbb{P} (A \cap B)}$$ I'm not sure how to get to this. Surely the probability of A occurring given A and B occurs is 1? Or, by the equation... $$\mathbb{P} (A | A \cap B)…
user78416
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Probability that 5 different faces come up twice each if 6 side die is rolled ten times?

Find the probability that 5 different faces come up twice each if 6 side die is rolled ten times? What methods should I apply here?
meiryo
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Minimum probability of biased coin to satisfy particular condition

Take $n$ pairs of integers $(x_i,y_i)$, $1\leq i\leq n$, selected independently as follows: Toss a fair coin $X$ and a biased coin $Y$ with $$\Pr[Y=\text{heads}] = p \neq 1$$ If $(X=\text{heads})$, then $x_i=-1$, otherwise $x_i=1$ If…
Jus12
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if two computers are playing tic-tac-toe, but they are choosing their squares randomly, what is the chance for X to win?

Tic-tac-toe is a children's board game that's notorious for draws. It's easy to write a program for either player (X or O) that always draws the game. I would like to know how the outlook changes if both players play completely randomly. Ie, X…
a person
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Understanding Bayes' Theorem

I worked through some examples of Bayes' Theorem and now was reading the proof. Bayes' Theorem states the following: Suppose that the sample space S is partitioned into disjoint subsets $B_1, B_2,...,B_n$. That is, $S = B_1 \cup B_2 \cup \cdots…
user1527227
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Calculating probability of next event given remaining count and range for each

(Apologies if my use of terms is off - I am not a mathematician by trade and what I did learn way back was in a different language) What I know: the total length of the stream, the body of possible events, the pop-count for each event, and the range…
500 - Internal Server Error
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The unfair subway

This is problem 24, "The Unfair Subway", in Mosteller's Fifty Challenging Problems in Probability with Solutions Marvin gets off work at random times between 3 and 5 P.M. His mother lives uptown, his girl friend downtown. He takes the first subway…
JasonMond
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Being the first to pick 1 of 2 cards out of a deck of 52 that will win you 1 million dollars.

Contestants in a game show are asked to from a line. One by one, each of them will be given one card (face up) from a deck of 52 until someone gets either an Ace of Spades or an Ace of Clubs. The first person who gets one of those cards will receive…
James Calase
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Probability of receiving a job offer on 3rd application

Suppose that when you submit a job application you have a probability of $0.1$ to receive an interview, and a job interview results in a job offer with probability $0.2$. Also assume you only submit one application at a time (i.e. you wait to know…
diteni1927
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Boy and girl probability

How many births must occur in a family, in order to have one boy and one girl with probability > 80%? Here is my attempt: If we have n births, all possible arrangements of Bs and Gs (GBGGBBGBG etc) are $2^{n}$. Of those, only one is GGGGG... (only…
Juan Manuel Prada
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