Career Development

# How To Calculate Probability

March 25, 2021

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 look at 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.

## How to calculate probability

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.
2. Identify the total number of outcomes that can occur.
3. Divide the number of events by the number of possible outcomes.

### 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 a possible outcome: you either roll a three or you do not 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 from 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 events 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.

## Odds vs. probability

Probability differs from determining the odds of something 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. You first determine the event you are looking for, which is rolling a three on the first try, and then you divide this number by the number of total outcomes you can get. Since the die has six faces, you can assume that you can have six total possible outcomes. So the probability will be one in six or a 1/6 chance of rolling a three on the first try.

Determining the likelihood of this event actually occurring is referred to as "the odds." The odds, or chance, of something happening depends on the probability. Probability represents the likelihood of an event occurring for a fraction of the number of times you test the outcome. The odds take the probability of an event occurring and divide it by the probability of the event not occurring.

So in the case of rolling a three on the first try, the probability is 1/6 that you will roll a three, while the probability that you won't roll a three is 5/6. The odds are represented by dividing these two probabilities: 1/6 ÷ 5/6 resulting in a 1/5 (or 20%) chance that you will actually roll a three on the first try. 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.

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

1. Determine each event you will calculate.
2. Calculate the probability of each event.
3. Multiply all probabilities together.

### 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. Since each event has a 1/6 chance of happening, you need to multiply 1/6 x 1/6 to get a 1/36 chance of rolling a six on one die at the same time you roll a six with the other.

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