Star basketball player Derrick Rose of the Chicago Bulls was named Most Valuable Player for the 2010-2011 NBA season.12 This table lists the number of baskets made of several types along with the number of attempts.

Use the implied percentages for each type of shot as probabilities to answer the following questions:
(a) Which opportunity has the highest expected value for Rose: two free throw attempts, one fIeld goal attempt, or one attempted 3-point shot?
(b) Which has larger variation in outcome for Rose: attempt a 2-point basket or attempt a 3-point basket?
(c) If his team is losing by 1 point near the end of a game, which of the following offers the bigger chance for a win (i.e., scoring 2 points): Rose attempts a fIeld goal or Rose attempts two free throws? Are any assumptions needed for this comparison?

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Type of Shot Free throw (1 point) Field goal (2 points) 3-point goal Made Attempts 476 711 128 1597 385