Table #1 : Elizabeth surveys 9th graders, 10th graders, and 11th graders in her school. She asks each student how many hours they spend doing homework each night. She records the responses in the table below. 1. How many 9th graders study 0-2 hours per night? 2. How many 11th graders study 2-4 hours per night? 3. What is the probability that a randomly chosen student (who was surveyed) is a 10th grader who spends 2-4 hours a night on homework? 4. What is the probability that a randomly chosen student is a 9th grader who spends 0-2 hours a night on homework? 5. What is the probability that a randomly chosen student will spend 2-4 hours a night on homework?

2-Way Tables These are tables that use both the rows and columns to display information. We can look at trends and determine if there is an association between the variables. Category Data CategoryData

Two Way Tables Two Types: Two Way Frequency Tables - give us the actual number of times an result occurs. Two Way Relative Frequency Tables – give us the relative frequency – or the ratio of a particular occurrence divided by a total of occurrences. The terms probability or percentage are also used and are found in a similar way to relative frequency.

20 children and adults were asked if they liked broccoli. The following table gives the results: YesNo Children38 Adults72

Vocab Joint Frequencies Marginal Frequencies

The first two things we will calculate are the Joint Relative Frequency and the Marginal Relative Frequency. Joint Relative Frequencies = Marginal Relative Frequencies= Marginal Relative Frequencies can also be found by adding the Joint Relative Frequencies in each row and column. (Add them and write them in the “margins”.)

YesNo Children Adults YesNo Children Adults Do the division and you get:

We can calculate the marginal relative frequencies this way: YesNo Children38 Adults72

Now we use this to calculate the Marginal Relative Frequencies: YesNoTotal Children Adults Total0.5 1

Used to find conditional probability Calculated by dividing the JRF by the MRF Conditional Relative Frequency

100 households were asked if they owned a cat and/or a dog: What is the Conditional Relative Frequency that a dog owner also owns a cat? CatNo Cat Dog1524 No Dog1843

First we calculate the JRF and MRF: Then we can calculate the CRF of a dog owner also owning a cat: CatNo CatTotal Dog No Dog Total

Given that they own a cat, what is the probability that they own a dog? CatNo CatTotal Dog No Dog Total

Example 1 Using the table below, what is the joint probability of a female that is involved in SGA? AthleticsMusic/ArtsSGAOtherTotal Male Female Total /30 = 0%

Example 2 Using the table below, what is the marginal probability of choosing someone who is involved with athletics? AthleticsMusic/ArtsSGAOtherTotal Male Female Total /30 = 50%

Example 3 Using the table below, what is the conditional probability given that a person is male, that they are involved in Music/Arts? AthleticsMusic/ArtsSGAOtherTotal Male Female Total /18 = 28%