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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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Find the probability of $\ A, B, C, D $

Suppose I have four events and I'll call them $\ A,B,C,D $ . This is the information I'm given: $$\ D \subseteq C \subseteq B \ \ ,P(A) = 0.59 , \ P(A \cap B \cap C \cap D) = 0.10 \\ P(A | D) = 0.50, \ P(A \cup B \cup C \cup D) =0.8\\ P(A \cap B^c…
bm1125
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confused about published answer to a conditional probability question

From https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/exams/MIT6_041F10_quiz01_s09_sol.pdf Alice and Bob both need to buy a bicycle. The bike store has a…
George
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Conditional probability Venn diagram

All of Adam's friends either jog or go to the gym, or possibly both. He knows 70% of friends jog and 35% gym. What percentage of Adam's friends go to the gym, but do not jog? My solution: $$P(\text{gym}\mid\text{no jog}) = \dfrac{P(\text{gym} \,…
Trogdor
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Probability of exactly one event occurring

Event A has probability of 0.7 and Event B has probability of 0.6. If A and B are independent, what is probability that exactly one occurs?
user199253
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Proof of Independence of two functions of random variables

If we have two random variables $X$ and $Y$ ($0
PatternMatching
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Probability of colored chips

Bowl I contains 7 red and white chips and bowl II has 4 red and 6 white chips. Two chips are selected at random and without replacement from I and transferred to II. Three chips are then selected at random and without replacement from II. a. What is…
Jonarie Ramos Vergara
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Conditional Probability regarding union

How would I solve this problem if the conditional probability for $\mathsf P(B \mid A)$ is not listed? Also, in Bayes' Theorem only intersection is listed, not Union. How would I find Union? $\mathsf P( A \cup B)$ if it is given that $\mathsf…
user161367
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Probability of guessing correctly after x tries with multiple right answers

I'm afraid I'm stuck on something that seems way too simple. I'm trying to calculate the chances of a brute force attack succeeding within a given time period. Simplified problem statement: Say I have 10 possible combinations (0-9) and 2 choices…
Boy Baukema
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Combinatorics and conditional probability

Assuming seven standard dice are rolled, what is the probability their sum equals 17? Show a general approach to solving this problem analytically, using conditional probability, combinatorics, etc
user160590
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Given values for $P(B\mid A\cup B)$ and $P(A\mid B)$. What is $P(B)$?

Let $A$ and $B$ be two independent events. How do you solve for $P(B)$? Since they are independent, we can say that $P(A\mid B) = P(A)$, but I don't know what much else we can extract from this information.
baba
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Chance of Double 1 or Double 6

I'm trying to fight out what are the chances of double 1 or double 6 I know that for 2 six-faced dice (aka 2D6) the probability would be 2/36. What are the chances for 3D6? 4D6? 5D6? and etc?
Eldwin
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Probability through sum of conditional probabilites

I have a vector $x$ of random variables and a finite set of classes $C$. Also $x$ has to belong to one class. In the context of classification problems I have the transformation $P(x) = P(x|c_1)P(c_1) + P(x|c_2)P(c_2) \ \cdots P(x|c_n)P(c_n)=…
elfeck
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A coin is tossed three times. What is the probability exactly two heads occur given that the first outcome was a head?

I have a very simple conditional probability question that I can't reason through. A coin is tossed three times what is the probability exactly two heads occur given that: a) The first outcome was a head The answer is obviously 1/2, since the…
William Smith
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Math A probabilty question

In Year 11 maths A there are three classes with 28,25 and 13 students in them respectively. A committee of three students is to be chosen. one from each class to represent a Maths Task Force. In how many ways can this group of three people be…
Jarrod
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Two questions on conditional exectation

Consider the random variable $X$ on $(\Omega,\mathcal{F},P)$ and let $\mathcal{G}\subset\mathcal{F}$. Q1. What is the difference between $E[X]=E[X|\{\emptyset,\Omega\}]$ and $E[X|\sigma(X)]$? Q2. Which of $E[X|\mathcal{F}]$ and $E[X|\mathcal{G}]$ is…
Freakalien
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