Question

at a high school, 84 students play video games during their free time. 106 students ride skateboards, and 29 students play video games and ride the skateboard. how many students engage in at least one of these activities in their free time? (enter your answer in the box below).

Explanation:

Step1: Use the principle of inclusion - exclusion

The formula for \(n(A\cup B)\) (the number of elements in either \(A\) or \(B\)) is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Let \(A\) be the set of students who play video games (\(n(A) = 84\)), \(B\) be the set of students who ride skateboards (\(n(B)=106\)), and \(n(A\cap B) = 29\) (students who do both).

Step2: Substitute the values into the formula

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Answer:

161