how to find the probability

Did you know that the basis of the probability formula stems from the idea of fractions where we find the part over the whole?

Jenn (B.S., M.Ed.) of Calcworkshop® teaching probability formula

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

It's true…

…and we're going to learn a whole lot more in today's lesson.

Let's go!

What is probability?

Probability is defined as the likelihood or chance that a specific event will happen.

And the probability of an outcome occurring is a value between 0 and 1 that describes the proportion of times an event will happen in a very long series of repeated attempts or trials. This means that if we know that an outcome will 100% happen, then the probability is 1, whereas if we know that a result will never occur, which means there is a 0% chance, then the probability is 0.

Now, assuming that all outcomes are equally likely, the probability of an event is the ratio of the number of outcomes that make up that event to the total number of possible outcomes as noted on Math Planet.

probability formula

Probability Formula

Throughout this lesson, and subsequent videos, we will learn the difference between independent events and dependent events, but I briefly want to discuss this idea now.

Independent events are when two events are independent when the outcome of the first event does not influence or affect the outcome of the second event, whereas dependent events are when two events when the outcome of the first event influences or affects the outcome of the second event.

So, for example, when we roll a fair die the probability of rolling a specific value is 1/6, and each roll is independent from the next.

Example – Choose a Random Number

For example, assume our sample space is the set of whole numbers from 1-20. If we randomly select one number from this sample space, the following events are defined as:

A: an odd number is selected
B: an even number is selected
C: a multiple of 5 is selected

Sample Space

sample space example odd numbers

A: Odd Numbers

sample space example even numbers

B: Even Numbers

sample space example for multiples of five

C: Multiples Of Five

How To Find Probability?

What is the probability that event A occurs? Event B occur? Event C occur?

Notice that there are ten numbers in A, ten in B, and four in C. So using our probability rule, we can calculate the following probabilities:

how to calculate probability

How To Calculate Probability

Probability Of A And B

Now, let's determine the probability of events A and B coinciding? Let's draw a Venn Diagram to investigate.

disjoint events in statistics

Disjoint Events In Statistics

Since odd and even numbers can't coincide, the probability of A and B occurring is zero.

Probability Rules

Now it's time to look at three essential probability rules:

The first two rules are called the Additive Rules for Probability.
The third rule is the Complementary Rule for Probability.

If A and B are two events, then the probability of A or B or both A and B occurring is

addition rule of probability

Addition Rule Of Probability

If A and B are two mutually exclusive (disjoint) events, then the probability of A or B or both A and B occurring is

addition rule for disjoint events

Addition Rule For Disjoint Events

The probability of not A is

complement in probability

Complement In Probability

Together we are going to walk through countless examples where we use our additive and complementary rules while creating Venn Diagrams and Tree Diagrams to find the probability.

Additionally, armed with our probability rules and our knowledge of combinations and permutations, we will:

Determine the probability for multiple events.
Extend our understanding to include new probability laws and theorems.
And even learn how to apply the additive rule for three events as shown to the right.

venn diagram and probability rules for three events

Venn Diagram And Probability Rules For Three Events

Probability Formula – Lesson & Examples (Video)

1 hr 25 min

Introduction to Video: Probability of an Event
00:00:27 – How do you find the probability of an event? (Examples #1-3)
Exclusive Content for Members Only

00:10:12 – Find the probability of two or more events (Examples #4-5)
00:20:33 – Find the probability by first using combinations and law of large numbers (Example #6)
00:27:47 – Additive Rules and Complementary Rules for Probability (Example #7)
00:41:59 – Create Venn diagrams and find the probability (Examples #8-9)
00:56:15 – Create Venn diagram for three events and find the probability (Example #10)
01:10:57 – Create a Tree diagram and find the probability (Example #11)
01:19:29 – Review of Probability Laws
Practice Problems with Step-by-Step Solutions
Chapter Tests with Video Solutions

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