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Topic: Conditional probability


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  Probability theory - Wikipedia, the free encyclopedia
Probability theory is the mathematical study of probability.
The probability that an event A occurs given the known occurrence of an event B is the conditional probability of A given B; its numerical value is
If the conditional probability of A given B is the same as the ("unconditional") probability of A, then A and B are said to be independent events.
en.wikipedia.org /wiki/Probability_theory   (838 words)

  
 Conditional probability - Wikipedia, the free encyclopedia
Conditional probability is the probability of some event A, given the occurrence of some other event B.
Marginal probability is obtained by summing (or integrating, more generally) the joint probability over the unrequired event.
In other words, the probability of A happening, given that B happens, is nil since A and B cannot both happen in the same situation; likewise, the probability of B happening, given that A happens, is also nil.
en.wikipedia.org /wiki/Conditional_probability   (409 words)

  
 Conditional probability: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-11-07)
In mathematics, a probability space is a set s, together with a σ-algebra x on s and a measure p on that σ-algebra such that p(s)...
Bayes theorem is a result in probability theory, which gives the conditional probability distribution of a random variable a given b in terms of...
In bayesian probability theory, the posterior probability is the conditional probability of some event or proposition, taking empirical data into account....
www.absoluteastronomy.com /encyclopedia/c/co/conditional_probability.htm   (787 words)

  
 Conditional distribution - Wikipedia, the free encyclopedia
X") is the probability distribution of Y when X is known to be a particular value.
From the definition of conditional probability, this is
The concept of the conditional distribution of a continuous random variable is not as intuitive as it might seem: Borel's paradox shows that conditional probability density functions need not be invariant under coordinate transformations.
en.wikipedia.org /wiki/Conditional_distribution   (270 words)

  
 Probability
If the probability of the found distribution is quite low given that the die is fair, then you may reject the hypothesis that the die is fair, and consequentially conclude that the die is biased.
Conditional probabilities are calculated when we need to know the likelihood of event A happening given that event B has already happened.
The binomial probability distribution arises in any situation where there are: (1) only two possible outcomes, (2) the number of trials or observations is fixed, (3) all the observations are independent, and (4) the probability of a success (p) is identical for each observation.
espse.ed.psu.edu /statistics/Chapters/Chapter7/Chap7.html   (4439 words)

  
 Conditional Probability
This problem describes a conditional probability since it asks us to find the probability that the second test was passed given that the first test was passed.
The probability that it is Friday and that a student is absent is 0.03.
The conditional probability of an event B in relationship to an event A is the probability that event B occurs given that event A has already occurred.
www.mathgoodies.com /lessons/vol6/conditional.html   (612 words)

  
 Conditionals
The notion of conditional probability entered probability theory at an early stage because it was needed to compute the probability of a conjunction.
Conditional desires appear to be like conditional beliefs: to desire that B is to prefer B to ~B; to desire that B if A is to prefer AandB to Aand~B; there is no proposition X such that one prefers X to ~X just to the extent that one prefers AandB to Aand~B.
Extending Jackson's account to conditional commands, the doctor said "Make it the case that either the patient is not alive in the morning, or you change the dressing", and indicated that she would still command this if she knew that the patient would be alive.
plato.stanford.edu /entries/conditionals   (14275 words)

  
 Kids.net.au - Encyclopedia Probability theory -   (Site not responding. Last check: 2007-11-07)
The sum of the probabilities of all the elementary events is one.
, the probability of either or both is given by the sum of the probabilities of the two events minus the probability of both.
The probability of some event happening knowing that another event happened before can be computed using conditional probability.
www.kidsseek.com /encyclopedia-wiki/pr/Probability_theory   (215 words)

  
 Bayes' Theorem
The probability of a hypothesis H conditional on a given body of data E is the ratio of the unconditional probability of the conjunction of the hypothesis with the data to the unconditional probability of the data alone.
The probability of a hypothesis conditional on a body of data is equal to the unconditional probability of the hypothesis multiplied by the degree to which the hypothesis surpasses a tautology as a predictor of the data.
The ratio of probabilities for two hypotheses conditional on a body of data is equal to the ratio their unconditional probabilities multiplied by the degree to which the first hypothesis surpasses the second as a predictor of the data.
plato.stanford.edu /entries/bayes-theorem   (7490 words)

  
 The Monty Hall Game
The conditional probability of A given B, P[AB], is the probability that A has or will occur given that B has occurred.
The probability of A and B (P[A and B]) is just (1/3)(1/3)=1/9 because if the car is behind Door 1 and the contestant has chosen Door 3 it is 100 percent certain that Monty Hall will show what is behind Door 2.
This means that the conditional probability that the car is behind Door 3 given that the contestant has chosen Door 3 and has been shown that there is a goat behind Door 2 is only l/3.
www.sjsu.edu /faculty/watkins/mhall.htm   (527 words)

  
 Implement Bayesian inference using PHP, Part 1
Conditional probability -- the probability of observing one event as a result of having observed another event -- is a potentially important factor in designing intelligent Web applications.
To compute the conditional probability of cancer given a positive test result, the doctor might tally the number of past cases where cancer and a positive test result occurred together and divide by the overall number of positive test results.
The probability of the ++ evidence key is the greatest for the d1 hypothesis.
www-128.ibm.com /developerworks/web/library/wa-bayes1   (5287 words)

  
 Conditional probability   (Site not responding. Last check: 2007-11-07)
A conditional probability is the probability of an event given that another event has occurred.
The probability of a total greater than 8 given that the first die is 6 is therefore 4/6 = 2/3.
Thus it would be read as "The probability that the total is greater than 8 given that Die 1 is 6 is 2/3." In more abstract form, p(AB) is the probability of event A given that event B occurred.
davidmlane.com /hyperstat/A129710.html   (207 words)

  
 Statistics Glossary - probability
Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1.
Like all probabilities, a subjective probability is conventionally expressed on a scale from 0 to 1; a rare event has a subjective probability close to 0, a very common event has a subjective probability close to 1.
In probability theory we say that two events, A and B, are independent if the probability that they both occur is equal to the product of the probabilities of the two individual events, i.e.
www.stats.gla.ac.uk /steps/glossary/probability.html   (1632 words)

  
 Conditional Probability
Conditional probability is a way of describing the influence of one event on another.
We say that the conditional probability of the event "winning the game" given the event "the first coin comes up H" is 3/4.
Note that according to these data, P(BA), the conditional probability of Bernie Williams getting a hit with a runner in scoring position, is higher than the unconditional probability of Bernie Williams getting a hit.
arnoldkling.com /apstats/conditional.html   (501 words)

  
 Math Forum - Ask Dr. Math Archives: High School Probability
My co-worker prefers to bet the same set of five lottery numbers every time, but I say that the probability is the same if you randomly select any set five numbers for the same period of time.
Calculate the probability that a baseball player batting.357 would hit safely in at least 56 straight games, during the course of a 162- game regular season, assuming 4 at bats per game.
We would like to know how to calculate the probability of having pulled a card from a subgroup in the deck by the Xth turn, where X increases from 1 to whatever.
mathforum.org /library/drmath/sets/high_probability.html   (993 words)

  
 Conditional Probability
The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred.
In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B).
To calculate the probability of the intersection of more than two events, the conditional probabilities of all of the preceding events must be considered.
www.stat.yale.edu /Courses/1997-98/101/condprob.htm   (681 words)

  
 Statistics Glossary - Probability
In probability theory we say that two events, A and B, are independent if the probability that they both occur is equal to the product of the probabilities of the two individual events.
The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values.
The probability density function of a continuous random variable is a function which can be integrated to obtain the probability that the random variable takes a value in a given interval.
www.cas.lancs.ac.uk /glossary_v1.1/prob.html   (3540 words)

  
 Conditional Probability   (Site not responding. Last check: 2007-11-07)
The probability that the card is a Jack "given that it is a face-card" is called a conditional probability.
In general terms, the "conditional probability" P[AB] is the probability that A occurs, given that B has occurred and is formally defined as:
The notation P[AB] is special shorthand that means "the probability of A, given that we know B has occurred." To obtain the answer for P[JackFace-card], we translate it into a ratio of the chances of both A and B happening to the chances of B happening.
www.bjmath.com /bjmath/probable/condit.htm   (486 words)

  
 SurfStat.australia   (Site not responding. Last check: 2007-11-07)
The probability of an event A may have to be recalculated if we know for certain that another event B has already occurred and A and B are not independent.
To achieve this the probabilities calculated previously need to be "rescaled" by dividing by their total, which was P(D) = 0.47.
The probability of C, given that D has occurred, is called the conditional probability and is written as P(CD).
www.anu.edu.au /nceph/surfstat/surfstat-home/3-1-4.html   (344 words)

  
 Conditional Probability Teasers   (Site not responding. Last check: 2007-11-07)
The teasers in question "ask for the probability that the objects of a certain pair both have some property when information exists that at least one of them does".
These problems can be solved by the application of conditional probability rules, but difficulties arise "in characterizing the conditioning event appropriately".
The output values are the percentages of the stipulated condition occuring in the sample and/or population.
www.cs.ualberta.ca /~jeffp/JavaClasses/java.html   (603 words)

  
 Conditional probability   (Site not responding. Last check: 2007-11-07)
For instance, in a modified blind search for the minimum of a non-negative function, the randomization strategy might be different when we already made some progress, and it might be different when we are ``stuck" in a non-optimal location.
The last condition merely says that B is an event that does have some chance of occurring.
Conditional probability of event A given event B is denoted by
math.uc.edu /~brycw/probab/books/smplbook/node19.html   (173 words)

  
 15MB of fame: Conditional probability: like watching magic tricks in slow motion
It is probably always a better idea to get your probability homework assigned by a professional than collect it from random weblogs.
The probability that one child is a girl already is 100%.
The "probably" should approach the subject with a little more fascination and humility, because it is extremely difficult and rewarding.
joshp.typepad.com /15/2003/11/conditional_pro.html   (2646 words)

  
 MATH250 - Printable Tutorial on Conditional Probability and Bayes' Formula   (Site not responding. Last check: 2007-11-07)
The probability of a student getting an "A" in the first quiz is 0.2.
Given that a student got an "A" in the first quiz, the probability that she will get an "A" also in the second quiz is 0.7.
The probability that a driver under the influence of alcohol will have an accident is 0.001.
www.math.ohiou.edu /~just/MATH250/cond1p.htm   (827 words)

  
 Conditional Probability
The probability of snow in the month of December, is different than the probability of snow in the month of July.
P(M\D) is the probability that a male is selected, given the fact that the person is a daily user.
P(D\M) is the probability that a daily user is selected given the fact that the person is a male.
www.omegamath.com /Data/d2.5.html   (1846 words)

  
 Conditional Probability   (Site not responding. Last check: 2007-11-07)
What Howard neglected to factor in with his commentary was the conditional probability of the situation.
When doing “poker math,” it’s important to not only look at the static probability of your opponent having a certain hand, but to also factor in the likelihood that your opponent could hold the hand you are worried about.
Conditional probability is what you should focus on if you want to reach the highest levels in poker.
www.cardplayer.com /poker_magazine/archives/showarticle.php?a_id=15005   (1322 words)

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