How To Calculate Probability (With Examples)

Have you ever checked the weather in the morning, heard there was an 80% chance of rain that day, and changed your outfit or your plans? If you have, then you’ve made a decision based on probability.

No matter what field or industry you’re in, you’ll have to use probability at some point. We use probability in our everyday lives, even if we don’t know it. Knowing how to calculate the probability of something and understanding what that means is a key skill for anyone.

Probability can help you in all facets of professional decision-making, from which marketing plan to go with or which approach will get you better sales numbers. The possibilities for using probability are endless, as long as you understand the basics.

We’re going to walk you through the basics of probability concepts and how to calculate them. This way, when you need to predict an outcome or make a decision based on a probability, you’re ready to rise to the occasion.

Key Takeaways:

• Probability is the likelihood that something will happen.

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn’t happen.

• Almost all professions involve the use of probability at one time or another. However there are certain jobs that rely heavily on calculating probability, such as statisticians, meteorologists, and healthcare professionals.

What is Probability?

Probability is how likely something is to happen. When you calculate probability, you’re approximating the chances of something happening and representing it with a precise number. So when the weather reports an 80% chance of rain, that means it’s 80% likely to rain that day. In other words, if it were to rain ten times, then eight of those times you’d get rain.

It’s impossible to predict things with absolute certainties, like the weather, but probability lets you get as close as possible. Whether you’re calculating something simple, like a coin toss, or something complex, you can use probability to help you understand the outcome like a sales forecast.

With probability, you’ll be able to make more educated decisions and back up your predictions with data to make compelling arguments. You can find ways to use probability in every part of your life, from simple day to day guesses to complicated sales predictions and marketing plans.

How to Calculate Probability

The great thing about probability is that it uses a simple formula, no matter what you want to gauge the likelihood of. If you can do some simple multiplication and division, you can calculate probability for any situation in no time. Here’s the basic formula for probability:

Probability of something happening = number of ways the event can occur ÷ total number of outcomes

Let’s break down how you can find the numbers you need and calculate the likelihood of an event. We’ll use the simple example of picking marbles out of a bag to make the process easy to understand, but probability can get much more complex if you need to handle big events.

1. Find your event. First, you need to figure out what variable helps you determine the probability. For example, if you have a bag of colored marbles and you want to figure out the probability of picking a blue one, that’s the variable you need to figure out. The outcome you want to calculate is how likely you’ll be to pull a blue marble from the mixed bag.

2. Find all the outcomes. Next, you need to find the total number of outcomes you can get in this situation. So, if your bag of marbles has 20 in all, you have 20 possible outcomes. This step determines what all of your possibilities are in this situation, not the specific outcome you want to calculate.

3. Find your desired outcome. You need to figure out how many chances there are for your desired outcome to happen. For this example, count how many of those 20 marbles are blue so you can figure out your chances of choosing a blue marble. For this example, say you count 11 blue marbles in the bag of 20 marbles.

4. Do your calculation. Now that you have all of the numbers you need, you can proceed with the next step and use the formula to find the probability. Divide 11 by 20, and you should get 0.55, or 55%. What does this number mean? It means the probability of you pulling a blue marble from the bag is 55%.

Odds vs Probability

When you’re talking about the likelihood of something happening, it’s easy to confuse odds and probability. People define the odds as the probability that something happens divided by the probability that it doesn’t happen.

Knowing the odds of an event happening is an excellent way to check the outcome you want. If you only pay attention to the likelihood of an event happening, you might miss the likelihood of it not happening.

For example, if the probability of something happening is 70%, you might think that’s a number close enough to 100% that you can rely on it. But, you must realize that it also means there’s a 30% chance that the event doesn’t happen. As you can see, calculating the odds factors in the chances of something happening and something not happening.

For example, take a look at the marble bag again. There are still 20 marbles in the bag, but this time you want to find the odds of choosing a green marble. There are two green marbles, so now you want to divide two by 20 and get 0.1. What does this number mean? It means that there’s a 0.9 probability that you don’t choose a green marble. To find the odds, you need to divide 0.1 by 0.9 to get 0.1111, or 11.11% odds.

How to Calculate Probability With Multiple Random Events

Unfortunately, not everything can be as simple as picking marbles out of a bag. Sometimes you need to calculate the probability of an event when multiple factors are going on. Luckily, you can calculate the probability of something happening when there are multiple events involved. It’s easy to do once you know how to get the probability for one event.

We’ll use something similar to the marble example again. Let’s say your company is awarding a prize if someone picks a marble that matches the company colors from a bag. The company colors are red and white, and you want to figure out the likelihood of one person picking red from bag A while another person playing picks white from bag B at the same time.

You know a bag of marbles comes with 500 marbles with 100 red, 250 white, 50 blue, and 100 green. So, you can calculate the probability of someone picking a red marble from bag A by taking 100 red marbles and dividing it by the 500 total marbles to get 0.2. For bag B, you take the 250 white marbles and divide by the 500 total marbles and get 0.5.

Now that you know the likelihood of these two events happening, you can calculate the probability of them happening simultaneously by multiplying the individual probabilities. So you’ll multiply 0.2 by 0.5 to get 0.1. This means that there’s a 10% chance that someone will pull a red marble from bag A while someone pulls a white marble from bag B.

Taking it one step further, you can also calculate the odds of this happening. To find the odds of this situation, you can divide 0.1 by 0.9 to get 11.11% odds that this happens.

Jobs that Involve Statistics and Probability

Some people are better at understanding, calculating, and interpreting probabilities than others. If you love figuring out the odds of something happening or love using data to make your decisions, you might want to look for a job that involves lots of statistics and probability. Here are a few careers that rely heavily on probability, predictions, and forecasting.

Just keep in mind that almost every job will require you to use probability and analysis, so even if you don’t pursue one of these careers, you’ll still be using statistics and probability in your work. It might just be less often than in these fields where probabilities rule the work you do every day.

• Statistician

• Meterologist

• Mathematician

• Market research analyst

• Financial analyst

• Operations research analyst

• Actuarial scientist

• Biostatistics

• Medical professions

• Risk assessment

• Public health

• Epidemiologist

• Professor

• Math teacher

Frequently Asked Questions

1. How do you calculate probability for multiple events?

To calculate probability for multiple events you must first calculate the probability of each independent event. Then you multiply the probabilities of each independent event with one another.

2. What is the difference between probability and odds?

The difference between probability and odds is that probability only factors in the likelihood of something happening, while odds also factors in the likelihood of it NOT happening. To calculate odds you take probability that something happens and divided it by the probability that it doesn’t happen.

3. Will I need to know about probability at my job?

Yes, you should know the basics about probability for your job. Although some jobs require a heavy use of probability, such as a statistician, every profession uses probability at some point or another. This is because the workplace is filled with so many dynamic situations, it is necessary for professionals to take into account multiple outcomes in any scenario.

Author

Amanda Covaleski

Amanda is a writer with experience in various industries, including travel, real estate, and career advice. After taking on internships and entry-level jobs, she is familiar with the job search process and landing that crucial first job. Included in her experience is work at an employer/intern matching startup where she marketed an intern database to employers and supported college interns looking for work experience.