The completed two-way frequency table from Example 1 is shown below. It shows the results of a survey designed to help the Student Council choose a school-wide activity.
Consider the following events that apply to a random student who participated in the survey.
[list]
[*][math]TEN[/math]: The student is in the tenth grade.
[*][math]TWELVE[/math]: The student is in the twelfth grade.
[*][math]FT[/math]: The student prefers a field trip.
[*][math]TS[/math]: The student prefers a talent show.
[/list]
Compare [math]P(TEN \vert FT)[/math] and [math]P(FT \vert TEN)[/math]. Are [math]TEN[/math] and [math]FT[/math] independent?
Compare [math]P(TWELVE \vert TS)[/math] and [math]P(TS \vert TWELVE)[/math]. Are [math]TWELVE[/math] and [math]TS[/math] independent?
Interpret the results.
