THEOREM OF TOTAL AND COMPOUND PROBABILITY.pptx

THEOREM OF TOTAL AND COMPOUND PROBABILITY

1. THEOREM OF TOTAL AND COMPOUND PROBABILITY

2. What Is Probability ? In simple terms, Probability is an expectations. It always lies within 0 to 1.00% to 100%) In our regular life, we face lot of problem, in which we supposed to use term like may be .., hope fully .. Etc. By definition it is the ratio of favorable number of cases over total number of cases. The concept of probability is necessary in work with physical biological or social mechanism that generate observation that can not be predicted with certainty.

3. Probability Of An Event :

4. Types of Probability : Theoretical Probability Probability which comes from thought experiment is called theoretical probability. • It is also called classical probability. It is calculated as follows: Experimental Probability Probability which comes from practical experiment is called experimental probability. • It is also called empirical probability. • It is found by repeating an experiment and observing the outcome. It is calculated as Subjective Probability Probability which comes from an educated guess is called subjective probability. It is found by observing and analyzing the past data. When the probability of something happening differs from person to person, it is likely a subjective probability.

5. Theorem Of Total Probability : Total probability or the law of total probability is a theorem which helps to calculate the total probability of an event. We calculate the total probability by taking into account several other distinct events that are disjoint from each other but are related to the event under consideration.

6. Bayes' theorem : The Bayes Theorem was developed and named for Thomas Bayes(1702-1761). Show the Relation between one conditional probability and its inverse. Provide a mathematical rule for revising an estimate or forecast in light of experience and observation.

7. Theorem Of Compound Probability : Compound probability which is also the joint probability is the probability of two events of an experiment occurring simultaneously. We can calculate the compound probability can be calculated for both independent as well as the dependent variable. For dependent variables, we use the concept of conditional probability specifically Bayes’ theorem. There are different formulas for calculating the two types of compound events: Say A and B are two events, then for mutually exclusive events: P(A or B) = P (A) + P(B). For mutually inclusive events, P (A or B) = P(A) + P(B) - P(A and B).