In​ 2016, among the top 100 grossing movies in a particular​ country, 16 were rated​ PG-13 and earned over​ $100 million. The number of movies that were rated​ PG-13 that earned less than​ $100 million was 29. The number of movies that were not rated​ PG-13 that earned less than​ $100 million was 39. What was the number of movies that earned over​ $100 million and that were not rated​ PG-13?

Answer:16Step-by-step explanation:Let,P = movie rated​ PG-13,P' = movie does not rated PG-13,E = movie earned over​ $100 million,E' = movie earned less than $100 million,According to the question,[tex]n(P\cap E)=16[/tex][tex]n(P\cap E')=29[/tex][tex]n(P'\cap E')=39[/tex]Since, [tex]n(P\cap E)+n(P\cap E')+n(P'\cap E')+n(P'\cap E)[/tex] = total movies[tex]16 + 29 + 39 + n(P'\cap E) = 100[/tex][tex]n(P'\cap E) = 100 - 84 = 16[/tex]Hence, The number of movies that earned over​ $100 million and that were not rated​ PG-13 would be 16.