Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [conditional-probability]

The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

From stat.yale.edu:

"The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B). If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by P(A and B) = P(A)P(B|A)."

Excerpt reference: Wikipedia.

2455 questions
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Monty Hall Problem with a Fallible Monty

Monty had perfect knowledge of whether the Door had a goat behind it (or was empty). This fact allows Player to Double his success rate over time by switching “guesses” to the other Door. What if Monty’s knowledge was less than perfect? What if…
Pseudoego
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How can I calculate the conditional probability of several events?

Could you inform me please, how can I calculate conditioned probability of several events? for example: P (A | B, C, D) - ? I know, that: P (A | B) = P (A $\cap$ B) / P (B) But, unfortunately, I can't find any formula if an event A depends on…
sewa373
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Probability that 2 OH NFL teams go 31 weeks w/o wins on the same day

I did this the obvious way, and my friend came back with a better idea. Can you guys adjudicate or improve on both? My way: The Cincinnati Bengals and the Cleveland Browns both won on Sunday for the first time in 46 weeks (says ESPN). That seemed…
Varun
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Marginalize probability with three variables

I am reading a book and saw the following equation: $$ P(X|\theta) = \sum_{z}P(X|z,\theta)P(z|\theta)$$ I know that that it is: $$ P(X) = \sum_{z}P(X|z)P(z)$$ But I don't know how the above equation with conditional probability and three variables…
Code Pope
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probability that random draws from the same pool will collectively select 90% of the pool

There are a total of 200 names on a list. 30 times names are selected from the full list. How many names should be selected each time to predict with 90% certainty that 90% of all the names will be selected at least once?
Daniel Timothy Virgin
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What's the probability that as I roll dice I'll see a sum of $7$ on them before I see a sum of $8$?

This question is from DEGROOT's PROBABILITY and STATISTICS. Problem Suppose that two dice are to be rolled repeatedly and the sum $T$ of the two numbers is to be observed for each roll. We shall determine the probability $p$ that the value $T =7$…
Silent
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contrapositive of probability

If P(A|B) = 95%, then is P(B'|A') also 95%? The subject is hypothesis testing. If the null hypothesis is true and there is a 95% probability that the data should pass the test, then does failing the test imply the null hypothesis is wrong with 95%…
TroyofHelen
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What does P(A|B)*P(A|C) simplify to?

Let's say we have a problem of predicting whether a storm is coming or not. We have a model P(storm is coming | how many clouds are outside), and have another model P(storm is coming | how scared the dogs are). My question in general is how to…
foobar
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Is there any way to merge two conditional probability distributions?

Is there any way to construct an expected conditional probability distribution of the form p(x|(y,z)) if I am starting with p(x|y) and p(x|z)? All variables are categorical. My specific problem deals with a DNA multiple-sequence alignment.…
adam.r
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What if $\mathbb{P}(A|B) = \mathbb{P}(B|A)$?

If we have $\mathbb{P}(A|B) = \mathbb{P}(B|A)$ then what is this special case called, and are there special properties? I'm interested in a simpler way of computing one of them and would like to take advantage of such properties.
m33lky
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What's the conditional distribution of X given X = Y

I'm in a setting in which X and Y are both $Beta(0.5, 0.5)$ and indipendent, that is $$f(x, y) = \frac{1}{\pi^2\sqrt{x(1-x)y(1-y)}}$$ What is the conditional distribution of X given Y = X? Normally i would substitute x to y in the density function…
Ivan
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conditional probability poisson and exponential

Suppose X and Y are independent random variables having the same Poisson distribution with parameter A, but where A is also random, being exponentially distributed with parameter 0. What is the conditional distribution for X given that X + Y = n? I…
user261409
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random variable conditioned on its own value

When I search online for conditional distributions, usually I find tutorials that one random variable is conditioned on another. I want to find some tutorial like the following exercise where there is a random variable that's conditioned on its own…
Salty Gold Fish
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What is the number of independent parameters in a family of conditional probabilities?

Suppose we have $n$ events $X_1, X_2, ..., X_n$ and we write down every possible conditional probability we can form from a subset of these events. So we're interested in all probabilities such as: $P(X_i)$, $P(X_i, X_j), \; i \neq j$ $P(X_i |…
Sjoerd Smit
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When a random variable has a distribution whose parameter is another random variable

Is there a standard name for a situation where a random variable follows a distribution whose parameter is another random variable ? For example a binomial(15,p) variable where the the p is distributed as beta(1,2), or a Poisson(Y) where Y is…
Joe King
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