Question

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 1

Answer:

16

Step-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,

$n(P\cap E)=16$

$n(P\cap E')=29$

$n(P'\cap E')=39$

Since,

$n(P\cap E)+n(P\cap E')+n(P'\cap E')+n(P'\cap E)$ = total movies

$16 + 29 + 39 + n(P'\cap E) = 100$

$n(P'\cap E) = 100 - 84 = 16$

Hence,

The number of movies that earned over​ $100 million and that were not rated​ PG-13 would be 16.