Introduction to Combinatorics and Probability

This course deals with probability, permutations, and combinations. The first section starts with a brief introduction to probability, It explains events, mutually exclusive and exhaustive events, conditional probability and its properties. The second section covers the multiplication theorem on probability, it also explains the meaning of independent Events. The third section covers Bayes Theorem and theorem of total probability. The fourth section covers permutation and its applications. The last section covers combination and its applications on probability.

15 topics

337 lectures

Educators

LL

Course Curriculum

40 videos

Powers and Polynomial

25 videos

Rational Numbers

11 videos

41 videos

Exponential Functions

15 videos

61 videos

Parametric Equations

5 videos

Introduction to Vectors

15 videos

15 videos

Polar Coordinates

5 videos

30 videos

Introduction to Conic Sections

23 videos

15 videos

Introduction to Combinatorics and Probability

16 videos

Introduction to Sequences and Series

20 videos

Introduction to Combinatorics and Probability Lectures

Introduction to Combinatorics and Probability

Independent Vs Dependent - Overview

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

Lily An

Introduction to Combinatorics and Probability

Independent Vs Dependent - Example 1

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

Lily An

Introduction to Combinatorics and Probability

Independent Vs Dependent - Example 2

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

Lily An

Introduction to Combinatorics and Probability

Independent Vs Dependent - Example 3

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

Lily An

Introduction to Combinatorics and Probability

Independent Vs Dependent - Example 4

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

Lily An

Introduction to Combinatorics and Probability

Independent Vs Dependent - Example 5

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

Lily An

Introduction to Combinatorics and Probability

Mutually Exclusive - Overview

In mathematics, a set of objects is mutually exclusive if it is impossible for more than one object to be an element of the set at the same time. For example, the numbers 2, 3, and 4 are mutually exclusive, because no number can be in all three sets at the same time.

Lily An

Introduction to Combinatorics and Probability

Mutually Exclusive - Example 1

In mathematics, a set of objects is mutually exclusive if it is impossible for more than one object to be an element of the set at the same time. For example, the numbers 2, 3, and 4 are mutually exclusive, because no number can be in all three sets at the same time.

Lily An

Introduction to Combinatorics and Probability

Mutually Exclusive - Example 2

In mathematics, a set of objects is mutually exclusive if it is impossible for more than one object to be an element of the set at the same time. For example, the numbers 2, 3, and 4 are mutually exclusive, because no number can be in all three sets at the same time.

Lily An

Introduction to Combinatorics and Probability

Mutually Exclusive - Example 3

In mathematics, a set of objects is mutually exclusive if it is impossible for more than one object to be an element of the set at the same time. For example, the numbers 2, 3, and 4 are mutually exclusive, because no number can be in all three sets at the same time.

Lily An

Introduction to Combinatorics and Probability

Mutually Exclusive - Example 4

In mathematics, a set of objects is mutually exclusive if it is impossible for more than one object to be an element of the set at the same time. For example, the numbers 2, 3, and 4 are mutually exclusive, because no number can be in all three sets at the same time.

Lily An

Introduction to Combinatorics and Probability

Mutually Exclusive - Example 5

In mathematics, a set of objects is mutually exclusive if it is impossible for more than one object to be an element of the set at the same time. For example, the numbers 2, 3, and 4 are mutually exclusive, because no number can be in all three sets at the same time.

Lily An

Introduction to Combinatorics and Probability

Probability With Combinations - Overview

In mathematics, a combination is a way to select items from a collection, such as a set or a deck of cards.

Lily An

Introduction to Combinatorics and Probability

Probability With Combinations - Example 1

In mathematics, a combination is a way to select items from a collection, such as a set or a deck of cards.

Lily An

Introduction to Combinatorics and Probability

Probability With Combinations - Example 2

In mathematics, a combination is a way to select items from a collection, such as a set or a deck of cards.

Lily An

Introduction to Combinatorics and Probability

Probability With Combinations - Example 3

In mathematics, a combination is a way to select items from a collection, such as a set or a deck of cards.

Lily An