Question

a winter resort took a poll of its 500 visitors to see which winter activities people enjoyed. the results were as follows: 348 people liked to ski, 309 people liked to snowboard, and 225 people liked to ski and snowboard. how many people in the poll liked to ski or snowboard?
of the 500 visitors polled, liked to ski or snowboard.
(type a whole number.)

Explanation:

Step1: Recall the formula

Use the formula $n(A\cup B)=n(A)+n(B)-n(A\cap B)$, where $A$ is the set of people who like to ski, $B$ is the set of people who like to snow - board, $n(A)$ is the number of people who like to ski, $n(B)$ is the number of people who like to snow - board, and $n(A\cap B)$ is the number of people who like both.

Step2: Substitute the values

Given $n(A) = 348$, $n(B)=309$, and $n(A\cap B)=225$. Then $n(A\cup B)=348 + 309-225$.

Step3: Calculate the result

$348+309 = 657$, and $657-225=432$.

Answer:

432