Short answers $(20$ marks$)$

$(1)$ Consider the following two descriptions of Mary:

$($i$)$ Mary loves to play tennis.

$($ii$)$ Mary loves to play tennis and, during the summer, averages at least a game a week.

Someone believes that description $($ii$)$ has a higher probability. Do you agree? Explain. $(4$ marks$)$

$(2)$ Joe invested $$1000$ in a stock, expecting the return over the following year tof be $6\%$ with the $90\%$ confidence interval being $2\%,10\%.$ However, the expected return of the stock over the next year turned out to be $4\%$ with the $90\%$ confidence interval being $-2\%,10\%.$ What types of confidence are presented in Joe's estimation of future return? Explain. $(6$ marks$)$

$(3)$ What is familiarity heuristic? List one investor behavioral bias that is related with familiarity. Explain why such behavior is biased. $(6$ marks$)$

$(4)$ The sales manager of a firm decides to double the number of flavor of its yogurt products from six to twelve, and believes this could attract more customers and expand their market share. What are the potential problems to her plan? Explain. $(4$ marks$)$