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 = \(\frac{3x}{4}\)
The number of students who like to go action movies = 2/3 of students who like to go movies = 2/3 of 3x/4 = \(\frac{6x}{12}\) = 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
= \(\frac{x/2}{x}\)
= 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
= \(\frac{4x}{10}\)
= \(\frac{2x}{5}\)
Hence, the fraction of students who like to go comedy movies
= Total students who like comedies/ Total students
= \(\frac{2x/5}{x}\)
= 2/5
