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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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Secret santa probability

26 people put their name in a hat. Each person picks a name out of the hat to buy a gift for. If a person picks out themselves they put the name back into the hat What is the probability of the last person picking themselves? I only ask this…
Curious
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Conditional Expectation of random sum of independent random variables

Let $Y=X_1+X_2+\dots+X_N$ where $X_1,X_2,\dots,N$ are jointly independent random variables, $X_1,X_2 ...$ identically distributed continuous random variables with finite expectation, and $N$ a discrete random variable with finite expectation. What…
dyuta
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Probability of two cot deaths in one family

In the UK, the probability of a cot death is about 1:8000. In the case of Sally Clark, two of her children died, apparently of cot death. But she was prosecuted for murder. An expert at her trial multiplied 1:8000 by 1:8000 to give 1:64000000, which…
Robert Campbell
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How to distinguish conditional probablity $P(A|B)$ and $P(A\cap B)$ in some practical problems?

A factory makes a type of computer monitor which are defective independently each with probability 1/20. To leave the factory, each monitor has to pass a test by a machine. The probability that the machine rejects a non-defective monitor is 1/10,…
liu yixin
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Difference between Pr(A | B) and Pr(A ∩ B)?

Suppose A is a group of people who uses motorbike and B is people who uses car , and A ∩ B is group of people who uses both motorbike and car. What is the probability of a person uses car , given that the person uses motorbike ? By…
i'm ashamed with what i asked
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Need help understanding conditional probability of continuous random variable conceptually

I need help understanding some stuff about conditional density. Here is an example from my book. A bird lands in a grassy region described as follows: $x ≥ 0$, and $y ≥ 0$, and $x + y ≤ 10$. Let $X$ and $Y$ be the coordinates of the bird’s landing.…
user911315
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Conditional probability and Bayes Rule.

There are k+1 coins in a box. When flipped, the $i$th coin will turn up heads with probability $\frac{i}{k} , i=0,1,...,k$. A coin is randomly selected and is then repeatedly flipped. If the first $n$ flips all result in heads, what is the…
fivestar
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P(A) given that P(A|B) and P(B) are known

Given that $P(A \mid B)$ is known, and $P(B)$ is known, how can $P(A)$ be calculated? I tried using the definition of conditional probability - $P(A \mid B) = P(A \cap B)/ P(B)$ - to solve for $P(A \cap B)$ but I don't know where to go from there.…
baba
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Cloudy and Sunny Days

In Freedonia, every day is either cloudy or sunny (not both). If it's sunny on any given day, then the probability that the next day will be sunny is $\frac 34$. If it's cloudy on any given day, then the probability that the next day will be cloudy…
Kevin
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Multiplication of conditional probabilities

Suppose 60% of people have a credit card, 37% of people have a debit card and 30% of people have neither a credit card or a debit card. Call these sets $A,B$ and $C$ respectively. I am assisting a friend of mine and her solution online says that the…
JessicaK
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conditional probability problem: picking chips

Urn 1 has three red chips and four blue chips. Urn 2 has two red chips and five blue chips. One chip is selected at random from each urn. If exactly one of them is a blue chip, what is the probability that the chip selected from urn 1 is the blue…
cgo
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Bayes Theorem for Conditional event that is an intersection of independent events.

I have a question regarding Bayes theorem, and independent intersected events as the conditional. How can this probability be decomposed using Bayes? $P(H \mid E \cap R)$ where $E$ and $H$ are independent events. Does that equal $P(H\mid E)\cdot…
stochasticcrap
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probability of tossing head

$A$ and $B$ are playing a coin tossing game. $A$ starts the game and if he gets a head the game is over and he wins $\$100$ cash. If he gets a tail $B$ will toss the coin and if he gets a head the game is over and $B$ will get $\$100$ cash. The game…
anı
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Help with a (subjective) conditional probability problem

I'm having trouble working out the conditional probabilities in this problem. I tell you that I'm about to toss a coin, which is either fair, or will land heads every time. You are told there is a 0.5 chance I pick either coin. Given this…
user144861
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What is the conditional mass function of $X$ given that $Y = i$?

First, let me explain the entire problem. Choose a number $X$ at random from the set of numbers $\{1, 2, 3, 4, 5\}$. Now choose a number at random from the subset no larger than $X$, that is, from $\{1,...,X\}$. (a) Find the joint mass function of…
Mlagma
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