Question

According to a survey of 100 people regarding their movie attendance in the last year, 40 had seen a science fiction movie, 50 had seen an adventure movie, and 40 had seen a horror movie. Moreover, 25 had seen a science fiction movie and an adventure movie, 5 had seen an adventure movie and a horror movie, and 15 had seen a science fiction movie and a horror movie. Only 5 people had seen a movie from all three categories.

Required:
a. Use the given information to set up a Venn diagram and solve it.
b. Complete the following sentence:

The survey suggests that ____________% of science fiction movie fans are also horror movie fans.

Answer 1

Kindly check attached picture ; 37.5%

Explanation:

Let:

S = number of science fiction movie viewers

H = number of horror movie viewers

A = number of adventure movie viewers

From the information given :

n(SnHnA) = 5

n(SnH) only = 15 - 5 = 10

n(SnA) only = 25 - 5 = 20

n(AnH) only = 5 - 5 = 0

n(S) only = 40 - (10+5+20) = 5

n(H) only = 40 - (10+5+0) = 25

n(A) only = 50 - (5 + 20 + 0) = 25

2.) % of science fiction movie to horror movie fans

Total Science fiction movie fans = n(S) = 40

Science fiction and Horror movie fans = n(SnH) = 15

[n(SnH) / n(S)] * 100%

(15 / 40) * 100%

0.375 * 100%

= 37.5%