Chances are (pun intended) you've encountered probability by now, but what exactly is a probability, and how do you calculate it? Probability is the likelihood of a specific event happening, like winning the lottery or rolling a 6 on a die. Finding probability is easy by using the probability formula (the number of favorable outcomes divided by the total number of outcomes). In this article, we'll walk you through exactly how to use the probability formula step by step, plus show you some examples of the Calculate probability formula in action.
Finding the Probability of a Single Random Event
Choose an event with mutually exclusive outcomes. Probability can only be calculated when the event whose probability you’re calculating either happens or doesn’t happen. The event and its opposite both cannot occur at the same time. Rolling a 5 on a die, a certain horse winning a race, are examples of mutually exclusive events. either the horse wins or it doesn’t.
Example: It would be impossible to calculate the probability of an event phrased as: “Both a 5 and a 6 will come up on a single roll of a die.”
Define all possible events and outcomes that can occur.
Let’s say you're trying to find the likelihood of rolling a 3 on a 6-sided die. “Rolling a 3” is the event, and since we know that a 6-sided die can land any one of 6 numbers, the number of outcomes is 6.
Divide the number of events by the number of possible outcomes.
This will give us the probability of a single event occurring. In the case of rolling a 3 on a die, the number of events is 1 (there’s only a single 3 on each die), and the number of outcomes is 6. You can also express this relationship as 1 ÷ 6, 1/6, 0.166, or 16.6%. Here's how you find the probability of our remaining examples:
Add up all possible event likelihoods to make sure they equal 1
The likelihood of all possible events needs to add up to 1 or to 100%. If the likelihood of all possible events doesn't add up to 100%, you've most likely made a mistake because you've left out a possible event. Recheck your math to make sure you’re not omitting any possible outcomes.
Represent the probability of an impossible outcome with a 0
This just means that there is no chance of an event happening, and occurs anytime you deal with an event that simply cannot happen. While calculating a 0 probability is not likely, it’s not impossible either.This is easy to calculate probability.