Of 158 consumers polled some like only action movies, some prefer just horror movies, and some like both. If 143 people like and only action and 62 like both how many people prefer only horror movies? Show your work

Question

Of 158 consumers polled some like only action movies, some prefer just horror movies, and some like both. If 143 people like and only action and 62 like both how many people prefer only horror movies? Show your work

Answer 1

Let:

A = action movies
H = horror movies
n(A) = number of people who like action movies
n(H) = number of people who like horror movies

According to the question, we have:
n(A) + n(H) - n(A ∩ H) = n(A ∪ H)

Given that n(A) + n(H) - 62 = 143 (143 people like and only action),
we can solve for n(H):
n(H) = 143 + 62
n(H) = 205

To find the number of people who prefer only horror movies, we subtract the number of people who like both (62) from n(H):
n(H – A) = n(H) - n(A ∩ H)
n(H – A) = 205 - 62
n(H – A) = 143

Therefore, 143 people prefer only horror movies.

Answer 2

Your answer is wrong, the correct answer is 53 people.

Answer 3

Apologies for the previous incorrect response.

Let's correct the solution:

Let:
A = Action movies
H = Horror movies
n(A) = number of people who like action movies
n(H) = number of people who like horror movies

According to the question, we have:
n(A) + n(H) - n(A ∩ H) = n(A ∪ H)

Given that n(A) + n(H) - 62 = 143 (143 people like and only action),
we can solve for n(H):
n(H) = n(A ∪ H) - n(A)
= 143 + 62 - n(A) (since n(A ∪ H) = n(A) + n(H) - n(A ∩ H))
= 205 - n(A)

Now, let's find the number of people who prefer only horror movies (n(H – A)):
n(H – A) = n(H) - n(A ∩ H)

We know that n(H – A) = n(A) + n(H) - n(A ∪ H)
So,
n(A) + n(H) - n(A ∪ H) = n(A) + n(H) - n(A ∩ H)
n(A ∪ H) = n(A ∩ H)

Therefore, n(H – A) = n(H) - n(A ∩ H) = n(H) - n(A ∪ H) = n(A) + n(H) - n(A)
n(H – A) = 205 - n(A) - n(A)
n(H – A) = 205 - 2n(A)

Given that n(A) = 143 (as mentioned in the question),
n(H – A) = 205 - 2(143)
n(H – A) = 205 - 286
n(H – A) = -81

However, it doesn't make sense for the number of people who prefer only horror movies to be negative. Therefore, it seems there may be a mistake in the given information or calculations.

Please double-check the provided data to verify, or provide any additional information if available.