A team of $8$ students has finished an investigation on the many uses of parabolas. They must select a single group member to present their findings to the class. They have only a single coin to make chance selections, but they can flip it as many times as necessary to select a student fairly. 

1. Using a single coin, find a fair way to select the presenter.

   Hint (a):

   There are a variety of possible methods. Make sure each student has an equally likely chance of being selected.

2. What is the smallest number of coin tosses needed to select a presenter fairly? Describe the method.

   Hint (b):

   Draw a tree diagram.
   How many times does the coin need to be flipped to get a sample space of $8$ equally likely outcomes?

3. Two of the group members realize they won’t be in class the day of the presentation because they are playing in a baseball tournament. Can a presenter still be chosen fairly with a single coin? Explain why or why not?

   Answer (c):

   Yes. Explanations/methods will vary.