Answer: 1) 1/2 students like to go to action movies,
2) 2/5 students like to go to action and comedies.
Step-by-step explanation:
Let the total number of students are x,
Thus, the number of students who like to go movies = 3/4 of total students = [tex]\frac{3x}{4}[/tex]
The number of students who like to go action movies = 2/3 of students who like to go movies = 2/3 of 3x/4 = [tex]\frac{6x}{12}[/tex] = x/2
Hence, the total fraction of students who like to go action movies = Number of students who like to go action movies / Total students
= [tex]\frac{x/2}{x}[/tex]
= 1/2
Now, the number of student who like to go comedy movie = 4/5 of the students who like to go action movies
= 4/5 of x/2
= [tex]\frac{4x}{10}[/tex]
= [tex]\frac{2x}{5}[/tex]
Hence, the fraction of students who like to go comedy movies
= Total students who like comedies/ Total students
= [tex]\frac{2x/5}{x}[/tex]
= 2/5
