Rock-Paper-Scissors, also called Roshambo, is a popular two-player game often used to quickly determine a winner and loser. In the game, each player puts out a fist (rock), a flat hand (paper), or a hand with two fingers extended (scissors). In the game, rock beats scissors which beats paper which beats rock. The question is: Are the three options selected equally often by players? Knowing the relative frequencies with which the options are selected would give a player a significant advantage. A study observed 119 people playing Rock-Paper-Scissors. Their choices are shown in Table 2.6.

Option Selected....Frequency
Rock ...........................66
Paper .........................39
Scissors .....................14
Total ........................119

(a) What is the sample in this case? What is the population? What does the variable measure?

(b) Construct a relative frequency table of the results.

(c) If we assume that the sample relative frequencies from part (b) are similar for the entire population, which option should you play if you want the odds in your favor?

(d) The same study determined that, in repeated plays, a player is more likely to repeat the option just picked than to switch to a different option. If your opponent just played paper, which option should you pick for the next round?