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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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Percentage of people who have good credit ratings given that their ratings will improve

Suppose that 75% of all people with credit records improve their credit ratings within three years. Suppose that 18% of the population at large have poor credit records, and of those only 30% will improve their credit ratings within three…
LadymadeStar
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what is the probability that is produced by the machine A?

A factory producing bolts manufactured by three machines A,B,C.Out of the total output 20%, 30%,and 50% of the production was produced by A,B,C respectively. Of the total of their output 5%, 4%, 2% are defective. A bolt is drawn at random from the…
user184583
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Conditioning continuous on discrete random variables

In a class hand-out of "review" material (which, in theory, should simply be concepts that we learned last semester in class but in practice contains a lot of stuff that we never covered due to what must be some sort of miscommunication as a result…
Ryan
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Conditional probability $P(A|B \cap C).$

I am trying to calculate $P(A|B\cap C).$ From my data set I have calculated: $P(A|B) = 0.58$ $P(A|C) = 0.44$ However, there is not enough data in the data set to calculate $P(A|B\cap C).$ Is there a way of combining $P(A|B) = 0.58$ and $P(A|C) =…
user2970105
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Conditional Probability | Please explain this answers

Can you please explain Why P(W2) is 4/9 ? Thanks..
Memo
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Probability of drawing 6 specific letters from a set of 144 with 21 draws

I know similar questions have been asked before, but I am struggling to find a method to calculate the probability for the situation below: I have a set of 144 scrabble tiles with the following letter distribution. 2 x , K, Q, X, Z 3 x B, C, F, H,…
gary
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Conditional Probability with boys and girls

Assume that a newborn baby is a girl with probability $p$ and a boy with probability $1-p$. Also assume that the genders of dierent newborns are independent of each other. Consider a person who has two children. Define the following two events: A =…
GivenPie
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Is this correct: $E(Y\mid X,U)=E(Y\mid X,U=0)P(U=0)+E(Y\mid X,U=0)P(U=1)$ if $U$ is a discrete taking values $0, 1$

Is this correct: $E(Y\mid X,U)=E(Y\mid X,U=0)P(U=0)+E(Y\mid X,U=0)P(U=1)$ if $U$ is a discrete taking values $0, 1$. Further more, can I do this, with the same $U$: Let $X=U+V$ $E(Y\mid X)=E(Y\mid X, U=0)P(U=0)+E(Y\mid X, U=1)P(U=1)$?
bankrip
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obtain conditional probability

Two common coins are tossed. a) Obtain the condiitional probability that both coins resulted in tails knowing that the first coin resulted in tail. b) What is the conditional probability that we obtains tails on both coins knowing that at least of…
nurainamardiah
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Probability in 2-Up; A coin is known

There is a game in Australia called 2-up in which you toss two coins in the air simultaneously. Suppose that when you throw the coins, one lands on the table and the other lands on the ground, so for now you can only see the coin on the table, and…
user133538
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Conditional probability of a continuous random event occurring over time

I may be expressing this in completely the wrong fashion, but please bear with me - I'm an engineer. Suppose I have an electric fuse in my house, and I know its probability of failure over time is distributed with probability density function $f(t)…
wobytides
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How to calculate the probability that one poker hand would beat another

I would like to know how one would go about calculating the probability that any one hand of poker is any better than that of one's opponent(s).
user115818
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condition probability

There is 3 random variables, A, B and C I know distribution P(C) and conditional distributions P(A|C) and P(B|C). How to find P(A|B)? I think it's necessary to integrate someone like this: $$ P(A|B) = \int P((A|B)|C) dP(C) $$ But how to find…
user1761982
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Express multiple conditional probability in terms of single conditional probabilities

I have to calculate/approximate the following multiple conditional probability: $$P(X|C_1,C_2,C_3)$$ with only $P(X|C_1)$, $P(X|C_2)$ and $P(X|C_3)$ given. Is it possible to express the above in terms of these single conditional probabilities only?…
niefpaarschoenen
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Two conditionally independent variables are conditional independent given $F$

Suppose X and Y are conditionally independent given Z. Suppose X and Z are conditionally independent given $F$,where $F\subset \sigma(Z)$. Prove that X and Y are conditionally independent given $F$.
Jack
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