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.
[list=1] [*]Find the totals of all the categories. [*]Compare [math]P(TEN \vert FT)[/math] and [math]P(FT \vert TEN)[/math]. [*]Determine if [math]TEN[/math] and [math]FT[/math] are independent. [*]Interpret the results for [math]P(TEN \vert FT)[/math] and [math]P(FT \vert TEN)[/math]. [*]Compare [math]P(TWELVE \vert TS)[/math] and [math]P(TS \vert TWELVE)[/math]. [*]Determine if [math]TWELVE[/math] and [math]TS[/math] are independent. [*]Interpret the results for [math]P(TWELVE \vert TS)[/math] and [math]P(TS \vert TWELVE)[/math]. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math II[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.