Question

A survey conducted among 560 youths of Kaski found that 320 liked to play football, 300 liked to play volleyball, and 500 liked to play at least one of the games. i. Find the number of youths who liked to play both games. ii. Find the number of youths who do not like to play both games.

A. i. 120, ii. 60
B. i. 120, ii. 40
C. i. 100, ii. 40
D. i. 100, ii. 60

Answer 1

To find the number of youths who liked to play both games, we can use the principle of inclusion-exclusion. The number of youths who liked to play both games is 120. The number of youths who do not like to play both games is 60. Hence, A) is correct.

Step-by-step explanation:

To find the number of youths who liked to play both games, we can use the principle of inclusion-exclusion. Let's denote the number of youths who liked to play football as A and the number of youths who liked to play volleyball as B. The number of youths who liked to play at least one of the games is given as 500, which we can represent as A ∪ B. We can use the formula:

A ∪ B = A + B - A ∩ B

Substituting the given values:

500 = 320 + 300 - A ∩ B

Simplifying the equation:

A ∩ B = 120

Therefore, the number of youths who liked to play both games is 120.

To find the number of youths who do not like to play both games, let's use the formula:

A' ∪ B' = (A ∪ B)'

Substituting the given values:

(A' ∪ B') = (A ∪ B)' = 500'

Simplifying the equation:

A' ∪ B' = 60

Therefore, the number of youths who do not like to play both games is 60.