College

A survey of 200 people yielded the following information: 96 people owned a Blu-ray player, 125 owned a microwave oven, and 78 owned both. How many people owned the following?

(a) a Blu-ray player or a microwave oven
(b) a Blu-ray player but not a microwave oven
(c) a microwave oven but not a Blu-ray player
(d) neither a Blu-ray player nor a microwave oven

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