ager. Each quarter Bernice has probability p of beating the market and probability 1p of failing to beat the market. The probability p is either 0, 1=2 or 1, depending on whether Bernice is, respectively, a bad, mediocre or good fund manager. Bernice's performance is independent from one quarter to the next. Hence, Bernice's performance can be correctly modelled as draws with replacement from an urn with 2 balls, where a proportion p of the balls correspond to good performance and a proportion 1 p of the balls correspond to bad performance. Adrienne, however, incorrectly thinks the balls are being drawn without replacement.

Suppose now that Adrienne doesn't know p, except that it can be either 0, 1=2 or 1 and it is equally likely to be any one of those three values. What does she conclude if she sees: (i) two good performances by Bernice? (ii) two bad performances by Bernice? (iii) one good and one bad quarter of performance? Are these conclusions correct? Explain the reasoning behind your answer and how the prediction of this model in (i) is related to the hot-hand fallacy in basketball.