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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 .

105859 questions
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Calculate the discrete probability density of $Z=XY$

$X$ and $Y$ are independent aleatory variables. $X$ : Poisson with 1 such as parameter $Y$ : Bernoulli with $\frac{1}{2}$ such as parameter Calculate the discrete probability density of $Z=XY$ $$P(Z=0)=P(\{X=0\} \cup \{Y=0\})=…
Elsa
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Calculating probability for unconventional 6 sided die

Let's consider this situation. We have $3$ different $6$-sided dice. The first die has five blank sides + one '$1$' side. The second die has four blank sides + two '$1$' sides. The third die has $4$ blank sides + one '$1$' side + one '$2$' side. In…
Jeph Gagnon
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Consequences of boy/girl probability disparity on population

In a population that grows, would a disparity in having a boy/girl probability cause the ratio of males to females tend to the same? e.g. if the probability of having boys was $.49$ and having a girl was $.51$ would that mean a growing population…
jimjim
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For any events A,B,C is the following true?

Is the following statement true? How? I'm having trouble seeing whether not it is true or false. $$P(A\mid B) = P(A\mid B \cap C)P(C\mid B) + P(A\mid B \cap C')P(C'\mid B)$$
britt
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People sitting in a round table.

I'm practicing for the actuarial examination and I found this problem that I couldn't solve. If someone can help me, I will be happy :-). Five Americans, three Germans and four Italians go to dinner together. They randomly sit at a round table…
DarioC
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subsets probability question

Consider a set $\Omega$ with $N$ distinct members, and a function $f$ defined on $\Omega$ that takes the values 0,1 such that $ \frac{1}{N} \sum_{x \in \Omega } f(x)=p$. For a subset $S⊆Ω$ of size n, define the sample proportion $p:= p(S)=…
rev
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Does $\Bbb E[X|Z]=\Bbb E[Y|Z]$ if $X,Y$ are identically distributed random variable?

Does $\Bbb E[X|Z]=\Bbb E[Y|Z]$ if $X,Y$ are identically distributed random variable, where $Z$ is a third random variable? Thank you!
Tony
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Probability for a sum of independent gamma random variables

Suppose we are told that the weight of each gum ball (in centigrams) is given by the gamma distribution function, with $α=25$ and $β=2$. Find the probability that 100 gum balls will go over the limit of a standard package of $52g$. I use central…
PersonaA
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Probability; can't understand the maths

For a random variable $x$, define a probability distribution $p[x=n]=c (3^n/n!)$ when $x=0, 1, 2, \dots$ and $p(x)=0$ otherwise. Find the value of $c$. My professor provided the solution $$ \sum_{x=0}^\infty \ c\frac{3^n}{n!}=1 $$ so $c\;e^3 =…
Mr Flint
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The eternally sleeping beauty. (Thought experiment regarding uniform distribution on the natural numbers)

A cousin of mine recently confronted me with a thought experiment that in essence contained an analogical situation to the following problem: Assume you are a beauty with the following properties: -You know there was a first day on which you woke…
uniquehorn
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Fair die: Probability of rolling $2$ before rolling $3$ or $5$

Independent trials consisting of rolling a fair die are performed, what is the probability that $2$ appears before $3$ or $5?$ There are $36$ cases if we take two trials like $11 12 13 14 15 16 ..21 22 23 24 25 26..31 32 33 34 35 36$ like this .…
RADHA GOGIA
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2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?

Situation A: Once only, I toss 2 identical fair coins and don't look at the outcomes. A truthful observer looks at one of the coins and tells me that at least one of the coins is a head. Situation B: Once only, I toss 2 identical fair coins and…
NotSuper
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Eddington's controversy simplified

I have been given the following probability problem: A, B and C are three people, who each independently speak the truth one of three times. A denies that B declares that C is lying. What is the probability that C is telling the truth? This…
Confused A level Student
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Probability of a result when spinning a disk

A circular disk is divided into $5$ equal segments. On spinning the disk a pointer always points to one segment. The segments contain pictures of $2$ bananas, $2$ lemons and one kiwi fruit. The disk is spun $4$ times. The probability of not getting…
twa14
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Expected value of Stock Price

Someone plans to use x dollars buying some stock share, the stock price is $a$ dollars per share now. One year later, the stock price will possibly increase to $ra$ or decrease to $a/r$ (r>1) which the probability is $p$, or remain the price now…
Charles Bao
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