Question

A local anime fan club surveyed its members regarding their viewing habits last weekend, and the following information was obtained: 35 members had watched an episode of Naruto, 48 had watched an episode of Death Note, 24 had watched both an episode of Naruto and an episode of Death Note, and 12 had watched neither Naruto nor Death Note. (Round your answers to three decimal places.)
(a) What percent of the club members had watched Naruto or Death Note?
(b) What percent of the club members had watched only Naruto?
(c) What percent of the club members had watched only Death Note?

Answer 1

Answer:

i think it is (b) What percent of the club members had watched only Naruto?

Step-by-step explanation:

Answer 2

Answer:

a) 83.099% of the club members had watched Naruto or Death Note.

b) 15.493% of the club members had watched only Naruto

c) 33.803% of the club members had watched only Death Note.

Step-by-step explanation:

First we find the number of students which each habit, treating the habits as Venn sets.

I am going to say that:

Set A: Watched an episode of Naruto.

Set B: Watched an episode of Death Note.

24 had watched both an episode of Naruto and an episode of Death Note:

This means that $(A \cap B) = 24$

48 had watched an episode of Death Note

This means that $B = 48$.

We have that:

$B = (B-A) + (A \cap B)$

In which B - A are those who watched only Death Note. So

$48 = (B-A) + 24$

$(B-A) = 24$

35 members had watched an episode of Naruto

This means that $A = 35$.

$A = (A-B) + (A \cap B)$

$35 = (A-B) + 24$

$(A-B) = 11$

At least one:

This is

$(A \cup B) = A + B - (A \cap B)$

So

$(A \cup B) = 35 + 48 - 24$

$(A \cup B) = 59$

Total number of students:

59 at least one, 12 none, so 71 total.

(a) What percent of the club members had watched Naruto or Death Note?

At least one, so 59 out of 71

59*100/71 = 83.099

83.099% of the club members had watched Naruto or Death Note.

(b) What percent of the club members had watched only Naruto?

11 out of 71. So

11*100/71 = 15.493

15.493% of the club members had watched only Naruto.

(c) What percent of the club members had watched only Death Note?

24 out of 71. So

24*100/71 = 33.803

33.803% of the club members had watched only Death Note.