Question

Of the eighth graders at the Paxton​ School, 99 played​basketball, 9 played​ volleyball, 10 played​ soccer, 1 played basketball and soccer​ only, 2 played volleyball and soccer​ only, 1 played basketball and volleyball​ only, and 2 played​ volleyball, basketball, and soccer.
Make a Venn diagram describing this information and use it to answer the following questions.

How many students were in the played at least one of the three sports?
How many students played only basketball?
How many students played volleyball and soccer, but not basketball?

Answer 1

Answer:

(a). 110

(b). 95

(c). 2

Step-by-step explanation:

In the question,

Number of students who played Basketball = 99

Number of students who played Volleyball = 9

Number of students who played Soccer = 10

Number of students who played Basketball and Soccer only = 1

Number of students who played Volleyball and Soccer only = 2

Number of students who played Basketball and Volleyball only = 1

Number of students who played Basketball, Volleyball and Soccer only = 2

So,

We can see from the Venn diagram shown below,

Number of students who played only Basketball = 99 - (1 + 2 + 1) = 95

Number of students who played only Volleyball = 9 - (1 + 2 + 2) = 4

Number of students who played only Soccer = 10 - (1 + 2 + 2) = 5

(a).

Number of students who played atleast one of three sports = Sum of all the sections in the Venn Diagram

= (95 + 1 + 2 + 1) + (4 + 2) + 5 = 110

(b).

Students who played Basketball only = 95

(c).

Number of students who play Volleyball and Soccer but not Basketball = 2