Probability and Statistics >Probability > Probability of a simple event happening

## Probability of a simple event happening: Overview

Simple events in probability have a certain chance of happening. For example, a 10% chance of rain today. When two or more probabilities are possible, they are added together to get the total probability. A 10% chance of snow and a 15% chance of hail would mean a 10% + 15% = 25% chance of bad weather. This article will show you how to **find the probability** of a simple event happening.

If you have another question type, check out the Probability Index for more question types, like multiple events at once.

## Probability of a simple event happening: Steps

**Sample problem #1**: In a recent survey, fifty percent of families in the US have no children living at home. Twenty two percent have one child. Twenty two percent have two children. Four percent have three children. Two percent have four or more children. If a family is **selected at random**, what is the **probability** that the family will have three **or** more children?

**Step 1:***Identify the individual probabilities and change the percents to decimals.*The question asks about the probability of a family having three or more children. In other words, you are looking for how many families have three or four children.

Four percent of families have three children, and 2% have four or more children. Our individual probabilities (as decimals) are**.04**and**.02**.**Step 2:***Add the probabilities together*.

.04 + .02 =**.06**.

**The probability is .06 or 6%.**

You’re done!

**Sample problem #2**: According to a 2013-2014 survey for the Humane Society, people owned 95.6 million cats.

- 46 percent—Percentage of owners with one cat.
- 31 percent—Percentage of owners with two cats.
- 23 percent—Percentage of owners with three or more cats.

If a cat owner is **selected at random**, what is the **probability** that the family will have fewer than three cats?

**Step 1:***Identify the individual probabilities and change the percents to decimals.*The question asks about the probability of a cat owner having fewer than three cats. In order words, you want to find how many cat owners have one or two cats.

46 percent have one cat and 31 percent have two cats. Our individual probabilities (as decimals) are**.46**and**.31**.**Step 2:***Add the probabilities together*.

.46 + .31 =**.77**.

**The probability is .77, or 77%.**

You’re done!

If you prefer an online interactive environment to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

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you make it easier than reading 15 pages of how to

I think you may have a misprint in the book with this same example. Under step 1. It says that 4% of families have two children.

Thank goodness that the same problem is on this site. I was trying five different ways to get 22% to equal .04.

Thank you for pointing that out! I will make a note for a correction in the new edition.

In Sample Problem #2, the percentages add up to 101%%

Thanks for catching that, Shane. It’s corrected!