Question

a winter resort took a poll of its 225 visitors to see which winter activities people enjoyed. the results were as follows: 165 people liked to ski, 105 people liked to snowboard, and 76 people liked to ski and snowboard. how many people in the poll liked to ski or snowboard? of the 225 visitors polled, liked to ski or snowboard. (type a whole number.)

Explanation:

Step1: Use the inclusion - exclusion principle

Let \(A\) be the set of people who like to ski and \(B\) be the set of people who like to snowboard. The formula for \(|A\cup B|\) is \(|A|+|B|-|A\cap B|\).
We know \(|A| = 165\), \(|B|=105\) and \(|A\cap B| = 76\).

Step2: Calculate \(|A\cup B|\)

\(|A\cup B|=165 + 105-76\)
\(=194\)

Answer:

194