Question

32 students play basketball and 25 Students play

volleyball . It is found that 13 students play both
games. Find the number of students playing at least
one game
dotos numbers Sets
n
و​

Answer 1

No. of students playing at least one game = 44
Explanation:
B = basketball; V = volleyball
n(B) = no of students playing only B
n(V) = no. of students playing only V
n(B∩V) = no. of students playing both B and V
Now:
32 students play basketball. Some of them could also be playing volleyball. Hence, the number of students playing only basketball will be 32 minus those that play both.
n(B) = 32 - 13 ............(Given that 13 play both games)
n(B) = 19
Similarly,
25 students play volleyball. Some of them could also be playing basketball. Hence, the number of students playing only volleyball will be 25 minus those that play both.
n(V) = 25 - 13
n(V) = 12
Thus, we have 19 students playing only B, 12 students playing only V and 13 students playing BOTH.
Clearly, the number of students that play at least one game is:
No. of students playing ONLY basketball +
No. of students playing ONLY volleyball +
No. of students playing BOTH
This can be given as:
n(B) + n(V) + n(B∩V)
= 19 + 12 + 13
= 44

Answer 2

44 students

Explanation:

Given parameters:

Number of students playing basketball = 32

Number of students playing volleyball = 25

Number of students playing both = 13

Unknown:

Number of students playing at least one game = ?

Solution:

Let us first find the number of students that play basketball only and volleyball only.

Number of students playing basketball only = 32 - 13 = 19

Number of students playing volleyball only = 25 - 13 = 12

So,

Least number of students that play at least one game = number of students that plays basketball only + number of students that plays volleyball only + number of students that plays both;

= 19 + 12 + 13

= 44 students