UCSS Math II 4.2.1 Example 3

A vacation resort offers bicycles and personal watercrafts for rent. The resort’s manager made the following notes about rentals: [list] [*][math]200[/math] customers rented items in all—[math]100[/math] rented bicycles and [math]100[/math] rented personal watercrafts. [*]Of the personal watercraft customers, [math]75[/math] customers were young (30 years old or younger) and [math]25[/math] customers were older (31 years old or older). [*][math]125[/math] of the [math]200[/math] customers were age 30 or younger. [math]50[/math] of these customers rented bicycles, and [math]75[/math] of them rented personal watercrafts. [/list] Consider the following events that apply to a random customer. [math]Y[/math]: The customer is young (30 years old or younger). [math]W[/math]: The customer rents a personal watercraft. Are [math]Y[/math] and [math]W[/math] independent? Compare [math]P(Y \vert W)[/math] and [math]P(W \vert Y)[/math] and interpret the results.

[list=1] [*]Determine if [math]Y[/math] and [math]W[/math] are independent. [*]Compare [math]P(Y \vert W)[/math] and [math]P(W \vert Y)[/math]. [*]Interpret the results. [/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.