Question

a winter resort took a poll of its 200 visitors to see which winter activities people enjoyed. the results were as follows: 93 people liked to ski, 81 people liked to snowboard, and 41 people liked to ski and snowboard. how many people in the poll liked to ski or snowboard? of the 200 visitors polled, \\(\square\\) liked to ski or snowboard (type a whole number.)

Explanation:

Step1: Recall the principle of inclusion - exclusion for two sets.

The formula for \(|A \cup B|\) (the number of elements in the union of sets \(A\) and \(B\)) is \(|A \cup B|=|A| + |B|-|A \cap B|\), where \(|A|\) is the number of elements in set \(A\), \(|B|\) is the number of elements in set \(B\), and \(|A \cap B|\) is the number of elements in the intersection of \(A\) and \(B\). Let \(A\) be the set of people who like to ski and \(B\) be the set of people who like to snowboard. We know that \(|A| = 93\), \(|B|=111\), and \(|A \cap B| = 41\).

Step2: Substitute the values into the formula.

\(|A \cup B|=93 + 111-41\)
First, calculate \(93+111 = 204\). Then, calculate \(204 - 41=163\).

Answer:

163