Final answer:
By applying the principle of inclusion and exclusion, it has been calculated that 108 people entertain from both audio and video media in the survey of 200 people.
Step-by-step explanation:
In the entertainment survey of 200 people, we are given that:
- 90 people enjoy video only.
- 12 people enjoy audio only.
- 10 people enjoy neither audio nor video.
Let's denote the number of people who enjoy both video and audio as x. To find the value of x, we can use the principle of inclusion and exclusion. Here's the formula to calculate the total number of people who enjoy either or both (union):
Total = People who enjoy video only + People who enjoy audio only + People who enjoy both - People who enjoy neither
By substituting the given values into the formula, we get:
200 = 90 + 12 + x - 10
We can now solve for x:
200 = 92 + x
So, x = 200 - 92
x = 108
Hence, 108 people entertain from both media.