# Probability of a Random Event: How to Find it

Probability and Statistics > Probability > Probability of a Random Event

## Probability of a Random Event: Overview

Part of the reason some people have trouble with probability questions is that it’s not always clear which technique to use to solve a problem. This particular how-to will guide you through solving random-event problems that give a percentage (e.g. 76% of Americans are in favor of Universal Health Care), then ask you to calculate the probability of picking a certain number (e.g. 3 people) and having them all fall into a particular group (in our case, they are in favor of health care). For more problem types centered around probability, return to the main probability index.

## Probability of a Random Event: Steps

Sample question: 76% of Americans support Obamacare. What is the probability that a randomly selected group of 3 people will all be in favor of Obamacare?

Step 1: Change the given percentage to a decimal. In our example:
76% = 0.76.

Step 2:. Multiply the decimal found in step 1 by itself. Repeat for as many times as you are asked to choose an item. For example, if you were to pick 3 items at random, multiply 0.76 by itself 3 times:

0.76 x 0.76 x 0.76 = .4389 (rounded to 4 decimal places).

That’s how to find the probability of a random event!

Tip: You may be wondering why the probability will continue to go down (0.76 x 0.76 x 0.76 x 0.76 x 0.76 x 0.76 = .19) when the question states 76% of people are in favor. If you think about the odds (76%) than means roughly 1 out of every 4 people you ask will NOT support Obamacare. It would be fairly impossible to ask 8 or more people in a row and have them all support Obamacare.