Probability and Statistics-Math is Fun

What is Probability- Meaning and Concepts?

Probability refers to the chance or likelihood of a particular event taking place. An event is a collection of outcomes and an outcome comes from an experiment.

P(A) = M/N, where M= number of outcomes favorable to occurrences of A and N= total possible outcomes.

Probability is a pure number and is greater than 0 and less than 1.

Mutually Exclusive Events are events in which two outcomes are such that nothing is common between them.

Independent Events are events in which occurrence of one is not dependent on the occurrence of the other.

What are the rules for Computing Probability?

Addition Rule- Mutually Exclusive Events

P(A U B) = P(A) + P(B)

Either A will occur or B or both will occur

Addition Rule- Not Mutually Exclusive Events

P(A U B) = P(A) + P(B) - P(A intersection B)

Both events are taken into consideration subtracting the intersection between them

If mutually disjoint:-  P(A intersection B) = 0

Multiplication Rule-  Independent Events

P(A intersection B) = P(A)*P(B)

Multiplication Rule-   Not Independent Events(Conditional Probability)

P(A intersection B) = P(A)*P(B/A)

What is Marginal Probability with an Example?

Marginal Probability is the the probability of one variable taking a specific value irrespective of the values of the others.

Contingency tables and margins are considered as marginal probability

The table below is an example:

1)What ratio of family is a buyer of a car?

80/200, this is marginal probability

2)What ratio of family is a buyer of a car and salary above 20k?

42/200, this is joint probability

3)A family has income of greater than 20k, what ratio of family is a buyer of a car?

42/80, this is conditional probability

What is Bayes Theorem with an Example?

Bayes Theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. It is used in situations when we have to switch probabilities and when false positives swamp the true positives.

It is mostly used in spam detection and linear discriminant analysis.

Mathematically Bayes Theorem is represented as:

Example of Bayes Theorem: