21
Jun
Bayes Theorem Of Probability. It describes the probability of an event based on prior knowledge of conditions that might be related to that event. Bayes theorem is a mathematical equation used in probability and statistics to calculate conditional probabilityIn other words it is used to calculate the probability of an event based on its association with another event. Bayes Theorem or as I have called it before the Theorem of Conditional Probability is used for calculating the probability of a hypothesis H being true ie. Simply put it is a way of calculating conditional probability.
Example 1 One of two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. It describes the probability of an event based on prior knowledge of conditions that might be related to that event. Here is a game with slightly more complicated rules. By design the probabilities of selecting box 1 or box 2 at random are 13 for box 1 and 23 for box 2. Bayes who was a reverend who lived from 1702 to 1761 stated that the probability you test positive AND are sick is the product of the likelihood that you test positive GIVEN that you are sick and the prior probability that you are sick the prevalence in the population. It can also be considered for conditional probability examples.
Eg- tossing a coin microscope2 or more possible result Experiment Outcome 2Outcome A particular result of the experiment.
Example 1 One of two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. This calculation is described using the following formulation. Bayes theorem is a formula that describes how to update the probabilities of hypotheses when given evidence. Bayes who was a reverend who lived from 1702 to 1761 stated that the probability you test positive AND are sick is the product of the likelihood that you test positive GIVEN that you are sick and the prior probability that you are sick the prevalence in the population. Example 1 below is designed to explain the use of Bayes theorem and also to interpret the results given by the theorem. It follows simply from the axioms of conditional probability but can be used to powerfully reason about a wide range of problems involving belief updates.