20.13 Making decisions. A six-sided die has two green and four red faces and is balanced so that each face is equally likely to come up. You must choose one of the following three sequences of colors:
RGRRR
RGRRRG
GRRRRR
Now start rolling the die. You will win $25 if the first rolls give the sequence you chose.
(a) Which sequence has the highest probability? Why? (You can see which is most probable without actually finding the probabilities.) Because the $25 payoff is fixed, the most probable sequence has the highest expected value.
(b) In a psychological experiment, 63% of 260 students who had not studied probability chose the second sequence. Based on the discussion of “myths about chance behavior” in Chapter 17, explain why most students did not choose the sequence with the best chance of winning.