As part of a lesson in survey design, Janette asks her study team of four students the following question: “Given the association between movie violence and crime, what kind of movie would you rather watch: romantic comedy or action?” All four indicate they would rather watch a romantic comedy. She states in her conclusion, “Obviously romantic comedies are the best.”

1. If the population of movie goers is actually equally split between those who prefer romantic comedies versus action movies, what is the chance of finding a group of four who unanimously prefer one genre over the other? Is it plausible?

   Hint (a):

   Draw a tree diagram.
   Note: This is similar to flipping $4$ coins because each person only has two choices.

2. Write a few sentences commenting on the validity of Janette’s methods and her conclusion.

   Hint (b):

   How was the question introduced?
   Also, how many choices were students given?