Question

32students play basketball and 25 student play volleyball. it is found that 13 student play both game .find the number of students playing at least one game​

Answer 1

Answer:

No. of students playing at least one game = 44

Step-by-step 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

See attached Venn Diagram to support understanding