In college basketball, a turnover is defined as losing possession of the basketball to the opposing team without scoring a basket. In theory, reducing the number of turnovers increases the likelihood of winning a game. The following table categorizes the number of wins and losses by the number of turnovers made by the Villanova Wildcats during two recent seasons.

Assume that a randomly selected game was chosen ­during one of the two seasons. What is the probability that the game

a. Was won by Villanova?

b. Had 9– 12 turnovers made by Villanova?

c. Was lost by Villanova, and Villanova made 13– 16 turnovers?

d. Was won by Villanova or Villanova made 5– 8 turnovers?

e. was won by Villanova, given that Villanova made 9– 12 turnovers?

f. had 21– 24 turnovers made by Villanova, given that ­Villanova lost the game?

g. Construct a decision tree for these probabilities.

h. Do winning and turnovers appear to be independent or dependent events for Villanova? Define Event A as a game with 13– 16 turnovers and Event B as a win. What conclusions can be drawn about these events?

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Turnovers Per Game Win Lose 5-8 9-12 13-16 17-20 21-24 17 5 22 10 4. 2 7 0