A student is taking a standardized test to apply to college. The test is multiple choice with four options (A, B, C, and D) for each question.

a. The student notices that he hasn’t selected option D for the past eight questions. What is the probability of this sequence of independent random events?

b. If there has been no D option for the past eight questions, what is the probability that the next answer will be D?

c. The student is sure that because there hasn’t been a D option for the past eight questions the next answer is probably going to be a D. What is the name of the fallacy he believes in? Why is his reasoning incorrect? How would you explain to him that he is wrong?