Chapter 3.8, Problem 26PPE

To determine

To find the number of people snowboard if 196 people ski and 154 people do both the activities ski and snowboard and the total surveyed people is 200.

Answer to Problem 26PPE

158 people snowboard.

Explanation of Solution

Given:

196 people ski and 154 people do both the activities ski and snowboard and the total surveyed people is 200.

Calculation:

Let A and B represents the people who ski and snowboard respectively.

Now given that,

  $n\left(A\cup B\right)=200,n\left(A\right)=196,n\left(A\cap B\right)=154$

Now,

  $\begin{array}{l}n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)\\ \Rightarrow 200=196+n\left(B\right)-154\\ \Rightarrow n\left(B\right)=200-42\\ \Rightarrow n\left(B\right)=158\end{array}$

Therefore 158 people snowboard.