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.

**Questions**? Post a comment and I’ll do my best to help!

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Wow I know I had these kinds of problems already but I didn’t understand it until now the light came on in my head. I wish they were all like this 1, 2 and then you are done. I like these that are short and sweet. Its just amazing how sometimes you have to do things over several times before it clicks in your head or at least thats how it works for me.