Question

According to a survey of 100 people regarding their movie attendance in the last year, 40 had seen a science fiction movie, 55 had seen an adventure movie, and 20 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. Construct a Venn diagram from the information provided. Include on your diagram the number of people in each region.
b. How many people saw at least one type of movie?
c. How many people saw only one type of movie?
d. What percentage of the people saw none of the three movie types?

Answer 1

Answer:

Check attached picture ; 75 ; 40 ; 25%

Step-by-step explanation:

s = science fiction movie

H = horror movie

A = adventure movie

From the information given :

n(SnHnA) = 5

n(SnH) only = 15 - 5 = 10

n(SnA) only = 25 - 5 = 20

n(HnA) only = 5 - 5 = 0

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

n(H) only = 20 - (10+5+0) = 5

n(A) only = 55 - (5 + 20 + 0) = 30

b.) Number of people who saw atleast one movie :

Sum of all numbers in the circles :

(5 + 20 + 5 + 10 + 5 + 30 + 0) = 75

c. How many people saw only one type of movie?

n(S) only + n(H) only + n(A) only

(5 + 5 + 30) = 40

d. What percentage of the people saw none of the three movie types?

Number of people who saw none of the movies:

100 - (Number of people who saw atleast one)

100 - 75 = 25

Hence, percentage who saw none :

(25/ 100) * 100%

(1/4) * 100%

= 25%