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Questions tagged [conditional-probability]

For questions on conditional probability.

Conditional probability is the probability that an event occurs given that another event has already happened. The probability of an event $A$ given another event $B$ is written as $P(A|B)$, and is related to the marginal and joint probabilities via $$ P(A|B)P(B)=P(A\cap B)$$

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Need check on conditional probability understanding

I'm selecting 164 items from a bag of 394. What is the probability that exactly 162 of these items will be green if there are 264 green items in the bag? I calculated this by multiplying the probability of selecting a green object on the first try…
mdrishan
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conditioning on continuous value

Is there a formula like this $$P(A)=\int P(A|x)p(x)dx $$ where $x$ is a continuous random variable? If yes, what is a good book for learning about this? Thanks!
hovnatan
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Conditional Probability (only given P(X|Y) and P(Y|X)

I need help with the following question: A study of the relationship between blood pressure and cholesterol level showed the following results for people who took part in the study: (i) of those who had high blood pressure, 50% had a high…
kekeke12
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Calculate conditional probability by conditioning on another event

I would like to calculate the conditional probability P(A|B). Can I calculate it base on conditioning on another set of mutually exclusive events {C1, C2, ..., Cn) ? i.e. something like: P(A|B) = P(A|C1)*P(C1|B) + P(A|C2)*P(C2|B) + ... +…
InTheSearchForKnowledge
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Conditional probability multiple conditions

I have a question about conditional probability. Is it true that $P(A|B|C)$ equal to $P((A|B)|C)$ equal to $P(A|(B|C))$?
An Ignorant Wanderer
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Conditional Probability question, depending on what colour ball is chosen, affects the 2nd event

A box contains 5 black and 8 white balls. A ball is removed and replaced by two of the other color and then a second ball is drawn. Calculate: (i) The probability that the second ball is white. (ii) The probability that both balls drawn are the…
Michael O' Driscoll
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conditional probability p(x|y) if y = x + e

Assuming x, y, $\epsilon$ are variables, and $y = x + \epsilon$, then: $$p(x=s|y=t) = p(t-s) = p(\epsilon) $$ Is that exist? It seems true but still don't know how to prove it formally. Can someone help me with the proof? Thx!
Wood
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Condition satisfied on a set is conditional probability

If I am told that $X(T)=a$ on $\{T\lt \infty\}$, a.s. Is that the same as the conditional probability $$P(X(T)=a|T\lt \infty)=1.$$ I know this is very basic but for some reason I haven't been able to find a concrete answer to this question.
Mper
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Conditional probability knowing probability of sick diagnosis and being sick and get sick diagnosis

Conditional probability knowing probability of sick diagnosis and being sick and get sick diagnosis I know that probability of sick diagnosis is 0.10 and i know that probability to be sick and get sick diagnosis is 0.08. I know that the probability…
pokeri
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Conditional Probability Notation random variable vs number

I am confused by the notation for the definition of a martingale. $E(X_{n+1}/X_n,....,X_1) = X_n$ I understand that $X_n$ here refers to the realized value but I don't understand why it is written as a capital $X_n$ and not as $x_n$. For example…
Jagol95
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Understand the "Naive Bayes" Assumption

I am trying to understand the Wikipedia page concerning the Naive Bayes classifier used in Machine Learning here. Supposing we have a vector $x = (x_1, \ldots, x_n) \in \mathbb{R}^n$. If we wish to know the probability that this vector belongs to…
IntegrateThis
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Conditional Probability. Drawing the ball from the urn.

Reading the paper I have encountered the following example: The urn that have been filled with black and white balls as follows. First, a ball is placed in the urn according to the outcome of a fair coin toss. If the coin toss for an urn produces…
user702441
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Conditional probability question concerning cards

A card is drawn from a standard pack. The dealer tells the players that it is a court card (jack, queen, king). what is the probability that it is either a jack or a red card? I've been stuck on this question since yesterday and I just feel like I…
BooScout
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Help with rearranging conditional probability

Given $\mathbb{P}(A^c|B^c) = \frac{1}{2}$, $\mathbb{P}(B^c|A^c) = \frac{1}{4}$, $\frac{\mathbb{P}(A)}{\mathbb{P}(B^c)} = \frac{1}{3}$. Calculate $\mathbb{P}(B)$. I don't get how to rearrange $\mathbb{P}(B)$ to solve it. Maybe there is some trick…
user577529
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Conditional probability, Likelihood

The probability of an issue being assigned to tester $A$ is $0.6$, and to tester $B$ is 0.4. The probabilty of tester A finding an error is $0.94$ and $0.98$ for tester $B$. If an error was found what is the probability that the issue was assigned…
app app
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