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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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Multiple conditional probabilities

Is it possible to calculate an expression $P(C_1,C_2,C_3|L_1,L_2,L_3)$ if I know only the individual $P(C_x)$ and all combinations of $P(C_x|L_y)$? How would I do that? Thanks!
Rob
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Conditional Distribution of a random variable in a Multinomial Distribution

Given $X_1,X_2,X_3$ ~ $Multinomial(n, \theta_1, \theta_2, \theta_3)$ what is the conditional distribution of $X_2$ given that $X_1=x_1$? My thoughts are: P($X_2=x_2$ | $X_1=x_1$) = $n-x_1 \choose x_2$ $\theta_2^{x_2}$ ($1-\theta_2)^{n-x_1-x_2}$ Can…
EggHead
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Question on using the integral of conditional probability to get unconditional probability

I'm trying to solve this problem in my homework assignment and I get different result from the answer. I know the answer is right, but at the same time I also don't see where I did wrong in my solution. So here's the problem: Let X and Y have a…
Vol_Smile
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Conditional Expectation of $M_n$ given $F_n$

Why is that the Conditional Expectation of $M_n$ given $F_n$ is equal to $M_n$ where $M_n$ is collection of the random variable $X_i$ where i runs from 0 to n and $F_n$ is the filtration at time n?
lakshmen
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Tossing two coins one fair and one double tailed.

If you toss a coin randomly from two coins Fair coin Double tailed If you got tails then what is the probability of heads being on the other side of same coin? My approach: Probably of picking fair or biased coin is 50/50. Case I: fair coin is…
Poudel89
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Find the probability that the ball drawn is white

Question :- From an urn containing $a$ white balls and $b$ black balls, a certain number of balls, $k$ is drawn and they are laid aside their colour unnoticed. Then one more ball is drawn. Find the probability that it is white. My approach:- Let $i$…
VOstro12
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7 pairs of socks, 7 different colours. Expected value of the number of days, in which 2 socks of the same colour are picked.

A student has 7 pairs of socks of 7 different colours. During 7 days he randomly picks 2 socks from the drawer (not necessarily of the same colour) and then doesn't put them back. Find the expected value of the number of days, in which 2 socks of…
John Doe
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Show that $P(B|A)=0.05$

Question:- A supplier of a certain testing device claims that his device has high reliability in as much as $P(A|B) = P(A^c |B^c ) = 0.95$, where $A$ : {device indicates component is faulty} and $B$ : {component is faulty} , $A^c$ : (Complement of…
VOstro12
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Help in solving Conditional Probability problem

I appreciate the help I have received in the past. Please help solve this problem. It holds the key to my understanding of other similar questions. "A box contains 7 marbles, numbered from 1 to 7 inclusive. Three marbles are randomly drawn from the…
Sylvester
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Let $G\sim\mathrm{Geometric}(p)$, $U\sim \mathrm{Unif}\{1,...,n\}$, and $G, U$ be independent. Determine the conditional probability $Pr(G=U|G \le n)$

I am struggling with the following conditional probability problem. Let $G \sim \mathrm{Geometric}(p)$, $U \sim \mathrm{Unif} \{1, \ldots ,n\}$, and $G$ & $U$ be independent. Determine the conditional probability $\mathrm{Pr}(G=U \mid G \le…
wacko_wanderer
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conditional probability within another condition

If given $P(Y|X)$, $P(X|Z)$, and $P(Z)$, can we find $P(Y|X,Z)$? I know that $P(X,Z)=P(X|Z)P(Z)$ and $P(Y|X,Z)=\frac{P(X,Z|Y)P(Y)}{P(X,Z)}$ but since $P(Y)$ is not given, it looks difficult for me to solve. Thanks in advance!
123mimi
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Probability conditioned by minimum

I have been working on this for a while now, but unfortunately I am not getting further with this, so I was hoping for some help maybe. Consider two independent continuous random variables $X_1$ and $X_2$ on the probability space $(\Omega,…
RPP
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What is f(x|y|z)?

update: I find the post on Double conditional probability @Joe referenced to be useful. But I am still trying to figure out some details. conditional probability states $$f(A) = \int f(A|z)f(z)dz$$ What happens when $f(A)$ is also a conditional…
Sara
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Can the result be 1? Finding the conditional PDF: X given Y=y.

I am struggling on a concept. If given a PDF: f(xy)=\begin{cases}y & 0 Y) I get the answer of being 2. I use a double integral to find it and have to…
Stat_wannabe
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Conditional probability of X given X+Y = n

Example 3.3 of Ross's book on Introduction to Probability models is If X and Y are independent Poisson random variables with respective means λ1 and λ2, calculate the conditional expected value of X given that X +Y = n. And the solution is quite…
Ram Zi
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