Question

A survey of 40 movie patrons revealed 18 said they saw the movie Scary Fractions and 32 said they saw the movie Dr. Venn and Mr. Diagram. Some people surveyed said they saw both movies. If all movie patrons saw one or both of the movies, how many saw both movies?

Answer 1

Answer:  10

Step-by-step explanation:

Let Event A = Patrons said they saw the movie Scary Fractions

Event B = Patrons said they saw the movie Dr. Venn and Mr. Diagram.

Given : $n(A)=18\ ;\ n(B)=32\ ;\ n(A\cup B)=40$

Using formula for sets ,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

We have ,

$40=18+32-n(A\cap B)\\\\\Rightarrow\ 40=50-n(A\cap B)\\\\\Rightarrow\ n(A\cap B)=50-40=10$

Hence, the number of patrons saw both movies = 10