Mathematics Stack Exchange
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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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Why does conditioning on this probability give me this other probability?

From Stochastic Processes by Ross At the top of page 75 (in the proof of lemma 2.3.4 on the bottom of page 74), the author writes (Summarized here): Let $\tau_1,...,\tau_n$ denote the ordered values from a set of $n$ independent uniform $(0,t)$…
Oliver G
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Probability of chosing a male and a female to compete.

Team A has $14$ females and $11$ males. Team B has $16$ females and $15$ males. The Teams are competing against each other. What is the probability a male and a female are chosen to compete? Team $A$ selecting a male is $\frac{11}{25}$ $\times$ Team…
Maths help
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Iterated conditional probability.

Let $P_R$ be a probability on $R$, let $\mathcal{Y}$ be the $\sigma$-algebra generated by the intervals that contain the positive reals $(x\geq 0)$, and let $\mathcal{Z}$ be the $\sigma$-algebra generated by the intervals that contain the negative…
Speltzu
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How to know whether to write P(I|F) or P(F|I) from a sentence.

I'm not sure if this qualifies as a mathematical question but I'm really confused. Take F to be the event “the fingerprints of the suspect match those at the crime scene” and I to be "the suspect is innocent". A prosecution lawyer argues that there…
Tingo Hugo
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What is probability of 2 independents events occurring given that another event has already occurred?

On Wikipedia on page relative to Conditional probability in section Statistical independence it is written following It should also be noted that given the independent event pair [A B] and an event C, the pair is defined to be conditionally…
schlebe
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Conditional probability from a sample

I would like to calculate the conditional probability $P(A|B)$ from the following sample of deaths from a certain year: \begin{array}{c|c|c} \hline & (B) \text{Smoker} & (C)\text{Not smoker} \\ \hline (A) \text{Tumor} & 231 & …
user3840
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Finding P{X = Y} where X~Geo(P), Y| X = i ~Binomial(i,p)

I need assistance figuring out how to address a specific question. I don't need the complete answer, just some guidance would be appreciated. Let $X$ be a geometric random variable with $P$ as the parameter. let $Y$, given $X = i$, a binomial random…
Sigma9
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Given a multicultural population, how to calculate the probability that both left and right neighbors are from different countries to middle??

Imagine a school with 100 students from nine different countries (a to i): A 50 students B 20 students C 15 students D 10 students E-I, 1 student from each For any randomly selected student Sitting in class, what is the probability that both her…
Jimbo78
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What does $P(X>7|X>5)=P(X>2)$ means? in an exponential distribution

What does $P(X>7|X>5)=P(X>2)$ mean in an exponential distribution? I know that the parameter for the distribution is $\lambda = 4$, but how can I verify that $$ P(X>7|X>5)=P(X>2)? $$ I only need to know how to write it as integral notation, but…
Valent
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Two boxes contain red and blue marbles; given color of picked marbles, probability of having chosen the first box

Problem: There are two boxes. The first one contains 5 red marbles and 7 blue ones. The second one contains 8 red marbles and 3 blue ones. One of the two boxes is chosen equiprobably, and two marbles are extracted, also equiprobably, from that…
mell_o_tron
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Conditional probability textbook question

I'm just looking for a confirmation. Textbook answer for this problem is $\frac{1}{18}$ but I'm getting $\frac{1}{20}$... You have 7 tickets to a baseball game. Three tickets are in the left field stands, 2 are behind home plate and 2 are near first…
hawks10
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Bayes network example

Given the following Bayes net: with $p(k=t)=.2$ $p(o=t)=.1$ $p(s=t|k=f,o=f)=.0$ $p(s=t|k=f,o=t)=.2$ $p(s=t|k=t,o=f)=.5$ $p(s=t|k=t,o=t)=.95$ how would I calculate $p(o=t|k=t)$? Intuitively I'd say it must be $0.1$, but if I calculate this as a…
random guy
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Probability of intersection of an event and a set of joint mutually independent events

I need some help to calculate the following joint probability: Let's consider a binary event $A=\{0,1\}$ with $P(A=1)=0.75$ and a set of finite events $B_i$, $i=1,\dots,n$, mutually independent. Let's also consider known the probabilities…
Luis Correia
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Conditional distribution

For my stats summer work, we were givin data to evaluate and perform problems with. They were the grades of a stats test between two class. A first period and last period class. I've gotten up to the conditional probability section. I've looked it…
Felipe
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Conditional Probability of Discrete Independent Events

Let $Y$ and $Z$ be discrete, independent random variables. Then $$P(Y = i | Y < Z) = P(Y = i)$$ Right? Because $Y$ and $Z$ are independent, the fact that $Y < Z$ doesn't tell us anything about $Y$, right? On the other hand, using the conditional…
StopReadingThisUsername
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