"In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred."
Calculation of probability when some conditions are already given.
Probability Basics: An introduction to probability which covers the basic terms and concepts, such as event, outcome, sample space, and probability distribution.
Conditional Probability: Understanding conditional probability and its notation, and how to calculate it using Bayes' theorem.
Independent and Dependent Events: How to determine whether events are independent or dependent, and how to calculate the probability of dependent events.
Bayes' Theorem: A formula that describes the probability of an event based on prior knowledge of conditions that might be related to the event.
Tree Diagrams: A diagram used to represent a probability problem, with the branches representing the possible outcomes and their probability.
Combinatorics: Techniques used to calculate the number of possible outcomes of a given event.
Permutations and Combinations: A method used to calculate the number of permutations and combinations for a given event.
Law of Total Probability: A formula used for finding the probability of an event that can occur through multiple mutually exclusive events.
Random Variables: Numeric values assigned to outcomes of a probability distribution.
Expected Value: The long-term average value of a random variable, and how it can be calculated.
Variance and Standard Deviation: Measures of the spread or variability of a probability distribution.
Joint Probability: The probability of two or more events happening simultaneously.
Marginal Probability: The probability of a single event without considering any other event.
Conditional Expectation: An extension of conditional probability, which is the expected value of a random variable given some other random variable.
Law of Large Numbers: A theorem that describes the behavior of the average of a large number of independent, identically distributed events as the number of trials increases.
Central Limit Theorem: A theorem that describes the distribution of a sample mean, which approximates a normal distribution with a mean and standard deviation.
Applications of Conditional Probability: Examples of conditional probability being used in real-life situations, such as medical diagnosis and weather forecasting.
Probability Distributions: An overview of probability distributions, such as binomial distribution, Poisson distribution, and normal distribution, and their properties.
Hypothesis Testing: A statistical test used to determine whether a hypothesis about a population is supported by the data or not.
Bayesian Inference: A statistical approach for making predictions and decisions based on probability theory and Bayes' theorem.
Simple conditional probability: The probability of an event occurring given that another event has already occurred.
Joint probability: The probability of two or more events occurring simultaneously.
Marginal probability: The probability of a single event occurring regardless of other events.
Conditional probability involving independence: The probability of an event occurring given that another event is independent of it.
Bayes' theorem: A formula that calculates the probability of an event given prior knowledge of related events.
Total probability theorem: A theorem that calculates the probability of an event occurring from knowledge of its conditional probability with respect to several mutually exclusive events.
Markov chains: A mathematical model that calculates the probability of transitioning from one state to another based on a stochastic process.
Expected value: The weighted average of all possible outcomes of an event based on their probability of occurrence.
Conditional independence: The probability of an event occurring given a set of conditions that are independent of each other.
Compound probabilities: The probability of a compound event, which involves the intersection or union of two or more simple events.
"This particular method relies on event B occurring with some sort of relationship with another event A."
"The conditional probability of A given B is usually written as P(A|B) or occasionally PB(A)."
"P(A|B) = P(A∩B) / P(B)"
"For example, the conditional probability that someone unwell (sick) is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75%."
"Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously."
"If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other."
"P(A|B) (the conditional probability of A given B) typically differs from P(B|A)."
"For example, if a person has dengue fever, the person might have a 90% chance of being tested as positive for the disease. In this case, what is being measured is that if event B (having dengue) has occurred, the probability of A (tested as positive) given that B occurred is 90% (P(A|B) = 90%). Alternatively, if a person is tested as positive for dengue fever, they may have only a 15% chance of actually having this rare disease (P(B|A) = 15%)."
"It should be apparent now that falsely equating the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies."
"It can be useful to reverse or convert a conditional probability using Bayes' theorem."
"Bayes' theorem: P(A|B) = (P(B|A)P(A)) / P(B)"
"Another option is to display conditional probabilities in a conditional probability table to illuminate the relationship between events."
"...conditional probability is a measure of the probability of an event occurring, given that another event has already occurred."
"...event B occurring with some sort of relationship with another event A."
"The conditional probability of A given B is usually written as P(A|B) or occasionally PB(A)."
"P(A|B) = P(A∩B) / P(B)"
"For example, the conditional probability that someone unwell (sick) is coughing might be 75%."
"...such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously."
"Another option is to reverse or convert a conditional probability using Bayes' theorem: P(A|B) = (P(B|A)P(A)) / P(B)"