If you are a visual person, a 2-way table is a great way to analyze information. This lesson shows you how to use a 2-way table to determine the independence of variables.

## Understanding Probability

Miquel is conducting research for his nutrition class. He is distributing a survey to all of the students in his school to determine if ice cream can make you taller.

He collects all of the data and puts it into a table like this:

Likes Ice Cream | Does Not Like Ice Cream | Totals | |
---|---|---|---|

Tall (>5.7) | 34 | 14 | 48 |

Short (<5.7) | 33 | 39 | 72 |

Totals | 67 | 53 | 120 |

In this table, you can see all of the different types of data Miquel collected and calculate probabilities based off of this information.

A **probability** is the likelihood or possibility of an outcome. For example, what is the likelihood that a randomly selected person over 5 ft. 7 in.

in Miquel’s school enjoys eating ice cream? Use the table to find your answer.You can take the total number of students at Miquel’s school and create a fraction with the number of people over 5 ft. 7 in. that enjoy eating ice cream. When you convert that into a percentage, you get your probability.

For this example, we take 34, which is the number of people over 5 ft. 7 in. that enjoy eating ice cream, and divide by 120, which is the total number of students at Miquel’s school.

34 / 120 = 28%. Therefore, you are 28% likely to meet a tall person that enjoys ice cream at Miquel’s school.So, the question is, does enjoying ice cream make you taller? Or, if you are taller, does that make you enjoy ice cream?To answer these questions, you will need to understand independence and conditional probability. In this lesson, you will learn how to use a 2-way table to determine if a probability is independent.

First, let’s look at independent and dependent probability.

## Independent ; Dependent Probability

When determining probability, you need to understand if the data you are collecting is being influenced by another event. There are two types of probability: independent and dependent.A **dependent event** is when one event influences the outcome of another event in a probability scenario.

For example, if you had a deck of cards and drew one card out of the deck, then this event would affect the probability of the next draw because you have fewer cards in your hand.An **independent probability** is when the probability of an event is not affected by a previous event. For example, if a student were to flip a coin once and get heads, then flip the coin again, his first flip would not affect the outcome of the second flip. The chances of getting heads or tails are always the same: 50/50.