Question

in 2019, 166,459 people (tourists and locals) attended the cirque du soleil shows in las vegas, 90,462 attended david copperfields magic show, and 33,419 attended both of those shows. how many people attended at least one of the shows? (enter your answer in the box below without using comma in your number).

question 4 3 pts

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 \(|A\cup B|\) (the number of elements in either \(A\) or \(B\) or both) is \(|A\cup B|=|A| + |B|-|A\cap B|\)

For the first problem:

Let \(A\) be the set of people who attended Cirque Du Soleil shows (\(|A| = 166459\)), \(B\) be the set of people who attended David Copperfield's magic show (\(|B|=90462\)), and \(|A\cap B| = 33419\)

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For the second problem:

Let \(A\) be the set of students who play video games (\(|A| = 84\)), \(B\) be the set of students who ride skate - boards (\(|B| = 106\)), and \(|A\cap B|=29\)

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Answer:

223502
161