Answer :
Step-by-step explanation:
To solve this problem, we can use the principle of inclusion-exclusion.
Given:
Total surveyed people (n) = 200
People owning a Blu-ray player (A) = 96
People owning a microwave oven (B) = 125
People owning both (A ∩ B) = 78
a) To find the number of people owning a Blu-ray player or a microwave oven (A ∪ B), we can use the formula:
A ∪ B = A + B - A ∩ B
A ∪ B = 96 + 125 - 78
A ∪ B = 217
b) To find the number of people owning a Blu-ray player but not a microwave oven (A - B), we can subtract the number of people owning both devices (A ∩ B) from the number of people owning a Blu-ray player (A):
A - B = A - A ∩ B
A - B = 96 - 78
A - B = 18
c) To find the number of people owning a microwave oven but not a Blu-ray player (B - A), we can subtract the number of people owning both devices (A ∩ B) from the number of people owning a microwave oven (B):
B - A = B - A ∩ B
B - A = 125 - 78
B - A = 47
d) To find the number of people owning neither a Blu-ray player nor a microwave oven, we can subtract the number of people owning both devices (A ∩ B) from the total surveyed people (n):
Neither A nor B = n - A ∩ B
Neither A nor B = 200 - 78
Neither A nor B = 122
So, the number of people owning the following is:
(a) a Blu-ray player or a microwave oven: 217
(b) a Blu-ray player but not a microwave oven: 18
(c) a microwave oven but not a Blu-ray player: 47
(d) neither a Blu-ray player nor a microwave oven: 122
