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.[br]Consider the following events that apply to a random student who participated in the survey.[br][list][br][*][math]TEN[/math]: The student is in the tenth grade.[br][*][math]TWELVE[/math]: The student is in the twelfth grade.[br][*][math]FT[/math]: The student prefers a field trip.[br][*][math]TS[/math]: The student prefers a talent show.[br][/list][br]Compare [math]P(TEN \vert FT)[/math] and [math]P(FT \vert TEN)[/math]. Are [math]TEN[/math] and [math]FT[/math] independent?[br]Compare [math]P(TWELVE \vert TS)[/math] and [math]P(TS \vert TWELVE)[/math]. Are [math]TWELVE[/math] and [math]TS[/math] independent?[br]Interpret the results.

[list=1][br][*]Find the totals of all the categories.[br][*]Compare [math]P(TEN \vert FT)[/math] and [math]P(FT \vert TEN)[/math].[br][*]Determine if [math]TEN[/math] and [math]FT[/math] are independent.[br][*]Interpret the results for [math]P(TEN \vert FT)[/math] and [math]P(FT \vert TEN)[/math].[br][*]Compare [math]P(TWELVE \vert TS)[/math] and [math]P(TS \vert TWELVE)[/math].[br][*]Determine if [math]TWELVE[/math] and [math]TS[/math] are independent.[br][*]Interpret the results for [math]P(TWELVE \vert TS)[/math] and [math]P(TS \vert TWELVE)[/math].[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.