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Adapted from Walch EducationUsing Two-Way Frequency Tables

Previously, you learned that there are two equivalent expressions for the conditional probability of B given A:

Conditional probability can be used to test for independence. Events A and B are independent events if or if Key Concepts7.2.2: Using Two-Way Frequency Tables2

For real-world data, modified tests for independence are sometimes used:Events A and B are independent if the occurrence of A has no significant effect on the probability of B; that is, Events A and B are independent if the occurrence of B has no significant effect on the probability of A; that is, Continued7.2.2: Using Two-Way Frequency Tables3

If A and B are two events from a sample space with P(A) 0, then the conditional probability of B given A in set notation is The conditional probability formula can be solved to obtain this formula for P(A and B): Concepts, continued7.2.2: Using Two-Way Frequency Tables4

A two-way frequency table is a frequency table that shows two categories of characteristics, one in rows and the other in columns. Each cell value is a frequency that shows how many times two different characteristics appear together.Two-Way Frequency Table7.2.2: Using Two-Way Frequency Tables5Typical Setup of a Two-Way Frequency Table7.2.2: Using Two-Way Frequency Tables6Category 1 of characteristicsCategory 2 of characteristics Characteristic 1 Characteristic 2Characteristic 1abCharacteristic 2cdWhen probabilities and conditional probabilities are calculated, then totals of characteristics are needed.

Note:7.2.2: Using Two-Way Frequency Tables7Category 1 of characteristicsCategory 2 of characteristics TotalCharacteristic 1 Characteristic 2Characteristic 1abCharacteristic 2cdTotalThe Student Council wants to host a school-wide activity. Council members survey 40 students, asking them to choose either a field trip, a dance, or a talent show. The table on the following slides shows the survey results, with the surveyed students numbered 140. Construct a two-way frequency table to summarize the data.Practice:7.2.2: Using Two-Way Frequency Tables8Table of Survey Results7.2.2: Using Two-Way Frequency Tables9(continued)StudentGradeActivityStudentGradeActivity110FT1112D212D1210TS310TS1311TS410FT1410FT511D1511D612D1610FT710TS1712D810FT1810FT910FT1912D1011TS2011TSKey: TS = Talent show, FT = Field trip, D = DanceTable of Survey Results, continued7.2.2: Using Two-Way Frequency Tables10StudentGradeActivityStudentGradeActivity2110D3112FT2210FT3210TS2312D3312D2411D3411D2511TS3511FT2612D3611FT2712D3711TS2810D3812TS2911D3911FT3011D4012TSKey: TS = Talent show, FT = Field trip, D = DanceSet up a table that shows Grade and Activity choice as categories, and all the different characteristics in each category.Step 17.2.2: Using Two-Way Frequency Tables11GradeActivity choiceTalent showField tripDance101112For each student, draw a tally mark that corresponds to that students grade and choice of activity in the appropriate cell of the data table. The complete tally table below shows the tally marks for all the students.Step 27.2.2: Using Two-Way Frequency Tables12GradeActivity choiceTalent showField tripDance101112

Create a two-way frequency table to show your count results (These results are frequencies). Step 37.2.2: Using Two-Way Frequency Tables13GradeActivity choiceTalent showField tripDance104821153612219Ms. DambrevilleThanks For Watching