Question

use a venn diagram to help solve the question below.
there are 85 girls that play volleyball and 70 girls that play basketball. there are 31 girls that play both sports.
a) draw a venn diagram to represent the situation.
b) how many girls play volleyball or basketball?
c) how many girls play just volleyball and not basketball?

Explanation:

Part (a)

To draw the Venn Diagram:

• Draw two overlapping circles. Label one circle "Volleyball" and the other "Basketball".
• In the overlapping region (the intersection), write 31 (the number of girls who play both sports).
• For the "Volleyball only" region, we'll calculate it later (for part c), but conceptually, it's the total volleyball players minus the intersection. Similarly, the "Basketball only" region is total basketball players minus the intersection.

Part (b)

Step1: Recall the principle of inclusion - exclusion

The formula for \( n(A \cup B) \) (the number of elements in set \( A \) or set \( B \)) is \( n(A) + n(B)-n(A \cap B) \), where \( A \) is the set of volleyball players and \( B \) is the set of basketball players.

Step2: Substitute the given values

We know that \( n(A)=85 \) (volleyball), \( n(B) = 70\) (basketball) and \( n(A\cap B)=31 \) (both).
So, \( n(A\cup B)=85 + 70-31\)

Step3: Calculate the result

First, \( 85+70 = 155\). Then, \( 155 - 31=124\).

Part (c)

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Answer:

124