Consider the Freddy model discussed in class. Freddy is observing (and making predictions about) two consecutive quarters of performance by Helga, a mutual-fund manager. Each quarter, Helga has probability p of beating the market, and probability 1 p of failing to beat the market. The probability p is either 0, 1/2, or 1. Helga's performance is independent from one quarter to the other. Hence, Helga's performance can be modelled correctly as draws with replacement from an urn with 2 balls (N = 2), where a proportion p of the balls corresponds to good performance, and a proportion 1 p of the balls corresponds to bad performance. Freddy, however, incorrectly thinks that the balls are being drawn without replacement.

(a) Identify which heuristic this model is intended to capture, and describe this heuristic in one sentence.

(b) Suppose Freddy knows for sure that p = 1/2, and that he has just observed one quarter of good performance by Helga. What is his prediction about Helga's performance in the next quarter? Explain your answer.

(c) Suppose Freddy doesn't know p. What does he conclude if he sees two good performances by Helga? Is this conclusion correct? Explain the intuition behind your answer.

(d) Explain how the above prediction of the model is related to the hot-hand fallacy in basketball.

(e) What does Freddy conclude if he sees one good and one bad quarter of performance? Is this conclusion correct?