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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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Probability of 5 or more unique successes in given population with known characteristics

To explain easier, I'll put it into a problem format. Assume the population is a deck of $60$ cards ($N = 60$). Of these cards, $35$ are blank and $25$ have letters on them. The quantity of cards with letters are known to be as…
finnsa
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Probability multiplication rule

Let $A$ and $B$ be events, not necessarily independent. The way I was taught was $\Pr(A \land B) = \Pr(A)\cdot\Pr(B|A)$. This is to say the probability of $A$ and then $B$ is equal to the probability of $A$ multiplied by the probability of $B$ given…
Shawn
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Probabability Paradox

Suppose you have $6$ fair weighted dice with all faces having $1$ to $6$. since the outcome is mutually independent and are disjointed sets, the probability of getting at least one six is $P(a)=6\cdot(1/6)$ by law of addition but if now there are…
Piyush Choudhury
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Probability of bit strings

Suppose you pick a bit string of length $10$. Find the probability that the bit string has exactly two $1$'s, given that the string begins with a $1$. Can someone please explain to me how to do it?
Zaima Asif
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How to Calculate Value with Conditional Probability?

How do you figure the average value of a variable affected by a repeated probable event ?. Suppose I have an experiment with input costs of $100$ for each trial: The first trial has a $90\ \%$ chance of success, the second $80\ \%$ and the third…
Holdrid
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Conditional Probability within regards to Discarding.

An urn contains four (4) red chips and six (6) white chips. Two (2) chips are drawn out and discarded and a third chip is drawn. What is the probability that the third chip is red? Would Hyper geometric Distribution be the best possible method for…
Aash
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expectations conditional probability

problem:After masks are produced by the factory, they appear in a test center, where they are tested for defects. Historically, only 10% of masks get a positive test result (meaning they are defective). Let T1= number of masks tested until first…
Silvija
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probability when knowing some factors

A farmer grows red and white flowers. In his warehouse, $\frac{1}{12}$ of the white flowers are roses. $\frac{2}{3}$ of the red flowers are roses. $25\%$ of all the flowers are roses. The rest are lily flowers. You randomly chose a flower from the…
Damien Hila Urban
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Finding conditional probability for 2 continuous random variables

For the given joint pdf of X and Y $$f(x,y) = 8xy, 0≤ y≤ x≤ 1$$ I need to find $$P(X<3/4 | Y<1/2)$$ I'm not quite sure whether my approach is right, but here's what I did. I found the marginal pdf of Y, which is $$4y - 4y^3, 0≤ y≤ 1$$ I know that…
MatCode
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Probability of distributing spades in a bridge game

STATEMENT In the card game bridge, the 52 cards are dealt out equally to 4 players—called East, West, North, and South. If North and South have a total of 8 spades among them, what is the probability that East has 3 of the remaining 5 spades? HINT:…
ArnuldOnData
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conditonal probability of matching numbers

STATEMENT 4 friends (Alex, Blake, Chris and Dusty) each choose a random number between 1 and 5. What is the chance that any of them chose the same number? (original problem here: https://www.mathsisfun.com/data/probability-events-conditional.html)…
ArnuldOnData
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Conditional Probability of Poisson Process

I have seen many questions on here regarding the conditional probability of the Poisson Process however I have not seen an option for the opposite i.e \begin{align} P(N_T = n | N_t = m) \end{align} where $T > t > 0$ and $n > m > 0.$ Could someone…
RareUsername
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Conditional Probability Given multiple independent events, Calculate P if possible

I am having difficulty in starting this question/which formula would be best to use and how would i be able to get the events as finite intersections. The questions is: P(A1 ∪ A2|A2 ∪ A3) = 5/6. Determine the probability, assuming A1-A5 are…
Aash
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How to assign probabilities to individual sample points in a tree diagram

Referring to the image , i have understood how probabilities are assigned to elements of sample space , S . Now , when we aim to calculate P(E|F) we consider F to be our new sample space for event E . So how do we assign the probabilities now to…
Anmol Bhatia
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Conditional probabilities with more than 1 vertical bar

I was looking at a reference today and saw a conditional probability written with more than 1 vertical bar $P(A|B|C)$. This is the first time I've seen something like this. Is this valid syntax. Is there another way to represent this?
user5965026
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