Determine whose method is the most fair, based on probability. Show your work. If needed, use a 6 × 6 array when analyzing Keenan’s method.
Explain why Gerard’s method isn’t fair.
Explain why Elena’s method would be unfair.


Elena, Keenan, and Gerard are planning a movie night, but can’t decide which movie to watch. Elena wants to watch an action movie, Keenan wants to watch a comedy, and Gerard wants to watch a science fiction movie. Since no one is budging on their movie preference, the three friends propose different methods for choosing the movie they’ll watch:

Elena suggests they call up her sister and have her make the choice for them.
Keenan suggests they roll two dice and find the sum of the dice. If the sum equals 2, 3, 4, or 7, then they’ll watch an action movie. If the sum equals 8, 9, or 10, then they’ll watch a comedy. If the sum equals 5, 6, 11, or 12, then they’ll watch the science fiction movie.
Gerard suggests they flip a coin two times. If both flips land on heads, then they watch an action movie. If both flips land on tails, then they watch a comedy. And if one flip lands on heads and one lands on tails, then they watch a science fiction movie.