Probability and Statistics > Probability > Probability of a Random Event

## What is a Random Event?

**A random event is something unpredictable.** As it is unpredictable, you can never give it an exact value / probability. For example, you couldn’t predict the probability of you falling down a flight of stairs in the next ten years, as that’s a completely random event. The opposite of random is deterministic, which means it can be calculated exactly. For example, your height can be calculated to the nearest inch, so height is deterministic.

## Probability of a Random Event: Overview

This particular example 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, check out 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.

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*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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