When it comes to studying mathematics, you’ve probably come across a lot of concepts that you just don’t see yourself using outside of the classroom. Maybe you’ve settled on learning them for your upcoming math test and then promising never to visit them again.
Well, that’s not exactly the case when it comes to the concept of probability. This mathematical calculation is actually something that will pop up in your life in many ways, whether you’re tossing a coin, watching the weather forecast, or betting on a sports game. Because it’s such an important aspect to understand, we’ve dedicated this guide to helping you make sense of probability.
Below, we’ll explain how to calculate probability and cover some basic probability rules and math tips. Once you get the hang of it, you just might be surprised how much you notice probability showing up in everyday life.
What is Probability?
First, let’s answer the question, what is probability? Probability refers to a mathematical calculation that falls under the umbrella of statistics. You use the equation to determine the likelihood of something happening.
Perhaps the easiest way to understand this is to think about flipping a coin. When you toss the coin in the air, you’re looking to determine the probability of an event. In this case, what are the chances of the coin falling on the tails side?
Ever since you were a kid, you’ve known there’s an equal 50-50 or 50% chance it will land on heads, but how exactly do we arrive at that percentage? By calculating its probability, of course!
Basic Probability Rules
Before diving into how to calculate the formula, we must first address the basic probability rules. While they might not make a whole lot of sense just yet, they will once you start putting probability into practice.
Rule 1: The probability of an event occurring is binary. It’s either 0 (it will never happen) or 1 (it is certain to happen). In other words, the possibility of an impossible event is 0. We use this formula to represent this math rule: A, 0 ≤ P(A) ≤ 1
Rule 2: All possible outcomes must add up to 1.
Rule 3: Also known as the Complement Rule, this rule reminds us that just as there is a probability that something will occur, there is also a probability something will not occur, and these are two separate events. This formula illustrates this rule: P(not A) = 1 – P(A)
Rule 4: This rule, called the Addition Rule for Disjoint Events, highlights the fact that some events can happen together while others cannot. If they can’t happen at the same time, they’re called mutually exclusive or disjoint. This is important to distinguish before making your calculation. This formula represents this rule: P(A or O) = P(A) + P(O)
Rule 5: An extension of the Addition Rule, this rule addresses events that are not necessarily disjoint. In this case, there is some overlap between the two events, so we use this formula: P(A or B) = P(A) + P(B) – P(A and B)
How to Calculate Probability
Once you understand the probability rules, it’s time to start calculating the probability of an event.
When it comes to figuring out how to calculate probability, you can begin by using this simple formula:
P(A) = (# of ways A can happen) / (Total number of outcomes)
You’re determining the probability of the event. In this example, what is the likelihood, or probability (P), that the event (A) will happen?
So let’s go back to the coin toss. How do we know that you have a 50% chance of landing on tails? Simply plug the numbers in below:
The possibility of tails= (1 way it can happen) / (2 outcomes)
That is, P(tails) = 1/2
The “1” means you can only get tails one way: when the coin lands on the tails side. And the “2” means that there are only two outcomes that can possibly occur: heads or tails.
Therefore, when you divide one by two, you get that 50% we all expected.
Probability in Everyday Life
When you know how to do probability in math, you’ll soon begin recognizing (and using!) it is everywhere.
Below are just a few of the many instances that involve the concept of probability:
- Determining the batting average of your favorite baseball player
- Predicting who might win the next presidential election
- Forecasting the chances of it raining this afternoon
- Playing the lottery
- Betting on a horse race
- Pulling slot machines
- Gambling on a card game
- And more!
The beauty of math is that once you learn certain concepts, you can apply them to many aspects of your everyday life. But we realize that learning math, especially more advanced concepts, is not always a walk in the park. It can be challenging, complicated, and sometimes even frustrating as you try to make sense of all those numbers and letters. If you’re struggling to keep up with your math studies or simply looking for some personalized instruction, we recommend signing up for private math lessons with TakeLessons.
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Maria Kusior