How To Calculate Probability

By Indeed Editorial Team

Updated May 24, 2022 | Published February 25, 2020

Updated May 24, 2022

Published February 25, 2020

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Probability is a mathematical calculation that can be applied to a variety of different applications. You might use probability when projecting sales growth, or you might use probability to determine the chances of acquiring new customers from a specific marketing strategy. Probability can also be applied to determining the chances of something occurring.

In this article, we'll explore what probability is, how to calculate the probability of single and multiple random events and the difference between the probability and the odds of an event taking place.


What is probability?

Probability is the likelihood of an event or more than one event occurring. Probability represents the possibility of acquiring a certain outcome and can be calculated using a simple formula. Probability may also be described as the likelihood of an event occurring divided by the number of expected outcomes of the event. With multiple events, probability is found by breaking down each probability into separate, single calculations and then multiplying each result together to achieve a single possible outcome.

Probability can be used in a variety of situations, from creating sales forecasts to developing strategic marketing plans, and it can be a highly useful tool for businesses who want to develop sound projections on things like sales, revenue and expected costs of operating a business.

Related: What Are Financial Projections? (And How To Use Them)

Probability formula

The probability formula defines the likelihood of the happening of an event. The formula to calculate the probability of an event is equivalent to the ratio of favorable outcomes to the total number of outcomes. Probabilities always range between 0 and 1. The general probability formula can be expressed as:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

or

P = n / N

Where:

  • P = Probability of an event occurring

  • n = Number of ways an event can occur

  • N = Total number of outcomes

Related: Types of Probability: Definition and Examples



How to calculate probability of a single event

Calculating probability requires following a simple formula and using multiplication and division to evaluate possible outcomes of events like launching new products, marketing to larger audiences or developing a new lead generation strategy. You can use the following steps to calculate probability, and this can work for many applications that fall under a probability format:

1. Determine a single event with a single outcome

The first step to solving a probability problem is to determine the probability that you want to calculate. This can be an event, such as the probability of rainy weather, or rolling a specific number on a die. The event should have at least one possible outcome.

For example, if you want to calculate the probability of rolling a three with a die on the first roll, you would determine that there is one favorable outcome: that you do roll a three.

2. Identify the total number of outcomes that can occur

Next, you need to determine the number of outcomes that can occur from the event you identified in step one.

In the example of rolling a die, there can be six total outcomes that can occur because there are six numbers on a die. So for one event—rolling a three—there may be six different outcomes that can occur.

3. Divide the number of events by the number of possible outcomes

After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes. For instance, rolling a die once and landing on a three can be considered one event. You can continue to roll the die, however, and each time you roll would be a single event.

So in the case of this example, you would divide the one event by the six possible outcomes that could occur. This results in a fraction: 1/6. So the probability that you will roll a three on the first try is one in six. You can further calculate the odds that you will roll a three on the first try by using the probability.

Related: How To Calculate Probability in Excel (With an Example)

How to calculate probability with multiple random events

Calculating probability with multiple random events is similar to calculating probability with a single event, however, there are several additional steps to reach a final solution. The formula for determining the probability of two events occurring is as follows:

P(A and B) = P(A) x P(B)

Where:

  • P(A and B)= Probability of both A and B events occurring

  • P(A) = Probability of event A

  • P(B) = Probability of event B

The following steps outline how to calculate the probability of multiple events:

1. Determine each event you will calculate

The first step for calculating the probability of multiple events occurring at the same time is to determine each of the events you want to work with. For instance, you might calculate the probabilities of rolling a six on two separate dice. Rolling each die separately represents one event. Using this example, we will calculate the probabilities of these two events occurring at the same time.

2. Calculate the probability of each event

Next, you can calculate the probability of rolling a six on one die and the probability of rolling a six on the other die. The probability for each event results in a 1/6 chance that you roll a six with either die. Using these results, you can then find the total probability of these two events happening simultaneously.

3. Multiply all probabilities together

Finally, you can multiply each probability together to get a total probability for all events that can occur. Using the dice example, you would calculate your total probability by multiplying the 1/6 chances you calculated in step two.

P(A and B) = 1/6 x 1/6 = 1/36 chance of rolling a six on one die at the same time you roll a six with the other

Related: How To Calculate Combination Probability (Plus Examples)

Odds vs. probability

Probability differs from determining the odds of something occurring. Determining the likelihood of an event actually occurring is referred to as "the odds." The odds, or chance, of something happening, depends on the probability. While the two mathematical concepts can be used together to solve various problems, you will need to calculate probability before determining the odds of an event taking place. The odds take the probability of an event occurring and divide it by the probability of the event not occurring.

To help illustrate this concept, use the example of calculating the probability of rolling a die and getting a three on the first roll. The probability is 1/6 that you will roll a three, while the probability that you won't roll a three is 5/6. Calculate the odds by dividing these two probabilities:

1/6 ÷ 5/6 = 1/5 (or 20%) chance that you will actually roll a three on the first try


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