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 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

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

**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!

Next example: Probability of an event happening.Like the solution? Check out our Practically Cheating Statistics Handbook, which has hundreds of step by step solutions for all kinds of probability and statistics questions.

**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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