Understanding probability

My lessons will make understanding probability very straightforward. Probability, which is the likelihood of something happening, is used daily in our conversation.

Understanding probability

For example, soon or later, most of us have asked ourselves the following questions: 

  • What is the likelihood that it is going to rain tomorrow?
  • What is the likelihood that when flipping a coin, it will land on tail?
  • What is the likelihood that a patient will die after a surgery?
  • What is the likelihood that you will die within the next five years?

The second question above is easier to answer.

Since a coin has two sides, it has 50% chance of landing on tail.

It also has 50% chance of landing on head.

The first and the third question are not easy to answer since they may require a solid understanding of the topic and some contextual information.

You may not be interested in the fourth question yet the company that sold you a life insurance policy will be interested in getting an answer to that question. The higher the likelihood that you will die within the next five years, the higher your premium.

Understanding probability is very important if you want to work for insurance companies, especially if you want to become an actuary.

My goal is to introduce you to the topic and help you develop an appreciation for probability as we explore some interesting situations and problems.


Any serious study of probability will start with a solid understanding of the fundamental counting principle, combination, and arrangement, which show you how to count.

Therefore, I strongly encourage you to start studying these. They will make understanding probability a lot easier.

Understanding probability with these great topics

Sample space and sample space diagram
Definition of sample space and showing the possible outcomes with a Venn and tree diagram.

Simple and compound events
Learn the difference between simple and compound events

Fundamental counting principle
You think you know how to count? It may not be as easy as you think. Find out right here!

Combinations
Suppose you want to buy 2 cars from a set of 4 distinct choices. How many different ways can this be done? Get the answer.

Solving word problems involving combinations
Learn to use the combination formula, the multiplication principle, and the addition principle.

Definition of factorial
Learn the meaning of factorial and how to find it.

Permutations
How many different ways can 3 people sit on 3 chairs? Get the answer here before you say that there is only one way.

Solving word problems involving permutations
Learn to use the permutation formula and the multiplication principle.

What is probability?
Learn the difference between classical probability, relative frequency of probability, and subjective probability

Probability line
Find out what a probability line is

Experimental probability
Learn the difference between theoretical probability and experimental probability.

Geometric probability
Learn to use a dartboard to find geometric probability

Probability of an event
Learn how to calculate the likelihood of an event.

Probability of compound events
Learn how to calculate the probability of at least 2 simple events.

Marginal probability
Learn how to calculate the probability using a contingency table

Conditional probability
Learn how to calculate the conditional probability using a contingency table

Mutually exclusive events
Learn about events that cannot occur together

Probability of independent events
Use a contingency table to find the probability of independent events

Probability of complementary events
Learn about complementary events and their probabilities

Joint probability
Learn to compute the probability of joint events

Addition rule for probability
Learn to find the probability of the union of two events

Useful calculators

Coin toss probability
When flipping a coin, what is the probability to get a head? Here coin toss probability is explored with simulated experimental coin toss data.

Factorial calculator
Get the factorial of any number.

Combination calculator
Find the number of combinations.

Permutation calculator
Find the number of permutations.

Dice roll calculator
Roll up to 4 dice to see the result. It is so realistic it is like rolling dice in real-life!


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