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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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How do I solve this probability

Anna writes down a random sequence created by the following process. She repeatedly rolls a fair 6-sided die. If the number she rolls is larger than all of the numbers she has previously rolled (if any), then she writes the new number down and then…
Bryan Hii
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conditional probability on two independent events

If A and B are independent events such that $Pr(A)=1/3$ and $Pr(B)>0$, what is the value of $Pr(A$ $\cup$ $B^c$$|B)=?$ From what I can understand , if we use the conditional probability formula , the numerator will be $Pr(A$ $\cup$ $B^c$ $\cap$ $B)$…
Kanika Adhikari
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Markov blanket and Conditional independence

$X$ --> $Z$ <-- $Y$ When using Bayes ball to check the independence of $X$ and $Y$ given $Z$, it is known that $P(X,Y|Z)\neq P(X|Z)P(Y|Z)$ in the above graph. (There is an example to help you to understand why. Considering that $X$: I am…
LaoMao
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This is about conditional probability

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is $0.13$ and the probability that the flight will be delayed is $0.18$. The probability that it will not rain and the flight will leave on time is $0.79$. What is…
banana
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$H(Y|X)=0$ if $Y=f(X)$ where $f$ is deterministic and $X$ is a continuous r.v.

I'd like to show that the conditional entropy $H(Y|X)$ is zero when $Y$ is deterministically determined by $X$ (i.e., $Y=f(X)$) and $X$ is continuous random variable. This claim is easy to prove when $X$ is a discrete r.v., but I feel kind of…
le4m
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Given that Rugen is the only one with six fingers on his right hand, what's the probability that Rugen's the perpetrator?

Blitzstein, Introduction to Probability (2019 2 ed), p 58, Example 2.3.10 (Six-fingered man). A crime has been committed in a certain country. The perpetrator is one (and only one) of the $n$ men who live in the country. Initially, these n men are…
R.jan
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How can i compute this probablity?

If we have: P(C) = 0.01 , P(!C) = 0.99 P(+|C) = 0.9 , P(-|C) = 0.1 P(-|!C) = 0.8, P(+|!C) = 0.2 How can i compute this probablity? P (C | (T1 and T2)). T1 and T2 are independent and T1 = +, T2 = +. This is where i've reached: P(+ and C) =…
Sajad Rastegar
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How to find conditional CDF?

The PDF of the random variable X is: $$f_X(x)=\begin{cases} 1\over3 & , -2\leq x\leq 1\\ 0 & , \text{otherwise} \end{cases}$$ I've observed that this is a uniform random variable (-2,1), I calculated the CDF: $$F_X(x)=\begin{cases} 0 & , x ⋹…
Andrei0408
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Work out a probability knowing only its conditional probabilities?

You are told that: $P(P) = 0.15$ $P(T|P) = 0.91$ $P(T|¬P) = 0.04$ $P$ and $T$ are not independent. Whats $P(T)$ ? I've been really struggling with this one. I've tried substituting a bunch of stuff into the multiplication rule $$P(A \cap B) = P(A)…
Max Randle
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If I roll 3 die at the same time and know that two of them are 3's, what is the probability the 3rd is also a 3?

This is not a homework problem, I'm just trying to better my understanding of this concept because it's so interesting yet counterintuitive to me and. I'm hoping someone will confirm that this is either correct or provide me with a logical…
PDef
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Event and pairwise independence

There are $n$ people for each $i ϵ \{1,\ldots,n\}$. $A_i$ is the event that a person $i$ experiences. Suppose $P[ A_i ] = \frac1{2i+1}$ , $A_i$ and $A_j$ are independent whenever $i \neq j$ . what are the lower and higher bounds for $P[ A_1 \cup…
VRD
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After many years, my Grandad told me his 'magic trick' isn't magic... but why does it work so often?

Take a standard pack of playing card, no jokers and no magic shop gimmicks. The 'Magician' invites you to name 2 cards, but without their suit; eg "two" and "queen" (ie but not "two of hearts" and "queen of spades") and says that he can make them…
MikeG
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If $B⊂A, P(A)=0.6, P(B)=0.4,$ what is $P(A∣B)?$

If $B⊂A, P(A)=0.6, P(B)=0.4,$ what is $P(A∣B)?$ $A. 2/5$ $B. 3/5$ $C. 1/3$ $D. 2/3$ now since B is a subset of A. I know $P(A \cap B) = 0.4 $ So I thought the answer is $1$ because $P(A | B)$ = $\cfrac {P(A \cap B)}{P(B)} = 1$ But the final answer…
user827508
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Interpret the conditional density $f(x\mid\theta)$, where $\theta$ is the parameter of the density.?

What does $f(x\mid\theta)$ denote? Isn't it interprets that- "here $\theta$ is known then what is the distribution of X for the known $\theta$?" Then why in the book which i am reading wrote that -- "the function $f(.\mid\theta)$ is assumed known…
ABC
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Calculating $ E[X\mid E[X\mid Y]]$

I have been wondering how to calculate $E[X\mid E[X\mid Y]]$. The lecturer gave this question after explaining how the error $X-\widehat{X}$ will always be perpendicular to any vector $Z-\widehat{X}$, which is in the linear space $S$ built from any…
Firas Abd El Gani
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