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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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conditional probability problem anomaly

This link: https://www.youtube.com/watch?v=5UQU1oBpAic, points to a youtube video that presents the following problem: suppose you have a chess match against an inferior opponent where 3/4 of the games end in a draw, and for the non-drawn games,…
user2661923
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Conditional Probability: $P(X|Y\leq y)=$ $\sum\limits_{k=1}^{y} P(X|Y=k)$?

Suppose $X \sim Binomial (Y,\delta)$. For the random variable $X$ can I compute the following conditional probability as follows? $P(X=x|Y\leq y)=$ $\sum\limits_{k=1}^{y} P(X=x|Y=k)$, where Y is a discrete random variable having the value of…
user3509199
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Is it true that $P(A|B) = P(A|C) \cdot P(C|B) $?

I think that $$P(A|B) = P(A|C) \cdot P(C|B) $$ is True. You are just transforming the information from $B$ through $C$. Is this correct and if it is, what's the name for this property?
Qwertford
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Sequential Conditional Probability

A woman lives in a country where only 1 out of 1000 people has the virus. There is a test available that is positive 5% of the time when the patient does not have it, negative 1% of the time when the patient does have it, and otherwise correct.…
Kong
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E and F being events, F is independent of E but E is not independent of F. Any example?

I was doing independent events and there I found that any two events(say $E$ and $F$) are independent when: $$P(F|E)=P(F)$$ provided $P(E)\ne0$ and $$P(E|F)=P(E)$$ provided $P(F)\ne0$ I'm having problem in understanding that why we have to work out…
Singh
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Conditional probability intuition

Regarding this question and its highest-voted answer: Conditional probability intuition. So I get the idea of using Venn-Diagrams and limiting our "universe" to a new subset, but what happens if we try looking at it with a tree diagram? Using this…
idanp
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Independence and conditional probability

Set 3 random variables A, B and C. A and C are independent, but B and C are dependent. Do we have $$P(A \mid B) = P(A \mid B, C)$$ (because A and C are dependent). If yes, how to prove it? Else, why not? Because I have an example in my lesson like…
moth
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Conditional Probability: Drawing a Spade followed by an Ace from a deck of 52 cards

My problem is as follows: Suppose you draw a card from a 52-card deck and see that the card is a spade. You then draw another card without replacement. What is the probability that the next card is an ace? I tried solving this question using…
Display Name
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True and False Positives

I am getting confused on what should be a fairly simple concept. A flu test gives true positives 90% of the time, and true negatives 85% of the time. 5% of people have the flu. We want to find the probability that a healthy person tests positive two…
mintteaplease
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Probablity question on independent events

If $A$ and $B$ are two independent events such that $\Pr(A)\gt 0$ , $\Pr(B)\gt 0$ and none of the two are certain events. Then what does $\Pr(A^\complement\mid B^\complement)$ equals? The answer is $1 - \Pr(A\mid B)$ isn't it? $1- \Pr(A\mid…
Shashank Shekhar
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How do YOU approach conditional probabilities?

So, I understand what they are but not perfectly and I'd like to. Take this example. We flip a fair coin. If it shows Heads, then we flip a fair 6-sided die, else, flip a 3-sided die. Let A be the event an even number is rolled. Find $P(A|H)$ When I…
Tingo Hugo
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Conditional distribution of $x_1\mid \sum_{i=1}^{n} x_{i}=t$

If $x_1, x_2, \ldots , x_n \sim \operatorname{Exp}(\lambda)$, then find $P(x_1 \mid \sum_{i=1}^{n} x_{i}=t)$. My approach is, $t=\sum_{i=1}^{n}x_i \sim \operatorname{Gamma}(n, \lambda)$, and $v=\sum_{i=2}^{n} x_{i} \sim \operatorname{Gamma}(n-1,…
Robin
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Basic probability: If $p(S| \neg G) = 0$, then $p(S|\neg G \& R)$ with $p(\neg G \& R) > 0 = p(S|\neg G) = 0$.

If $p(S|\neg G) = 0$, then $p(\neg G \& R) > 0 \implies p(S\mid \lnot G\& R)=0$. Could someone please prove this? Many thanks in advance.
Mijito
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Does the tail got a 50-50 chance of appearing itself if one of two coins already identifies itself as heads

Two coins are tossed once, where E: tail appears on one coin, F: one coin shows head. The event 'F' refers that it had happened already. The question is what is the probability of finding one tail —the event 'E' happening— from one of two coins if…
Venkatesa M.G.
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