NBA draft lottery. Professional basketball teams holda “draft” each year in which they get to pick the bestavailable college and high school players. In an effort topromote competition, teams with the worst records getto pick first, theoretically allowing them to add betterplayers. To combat the fear that teams with no chance tomake the playoffs might try to get better draft picks byintentionally losing late-season games, the NBA’s Boardof Governors adopted a weighted lottery system in 1990.Under this system, the 11 teams that did not make theplayoffs were eligible for the lottery. The NBA prepared66 cards, each naming one of the teams. The team withthe worst win-loss record was named on 11 of the cards,the second-worst team on 10 cards, and so on, with theteam having the best record among the nonplayoff clubsgetting only one chance at having the first pick. The cardswere mixed, then drawn randomly to determine the orderin which the teams could draft players. Suppose thereare two exceptional players available in this year’s draftand your favorite team had the third-worst record. Use asimulation to find out how likely it is that your team getsto pick first or second. Describe your simulation carefully.

Question

NBA draft lottery. Professional basketball teams hold
a “draft” each year in which they get to pick the best
available college and high school players. In an effort to
promote competition, teams with the worst records get
to pick first, theoretically allowing them to add better
players. To combat the fear that teams with no chance to
make the playoffs might try to get better draft picks by
intentionally losing late-season games, the NBA’s Board
of Governors adopted a weighted lottery system in 1990.
Under this system, the 11 teams that did not make the
playoffs were eligible for the lottery. The NBA prepared
66 cards, each naming one of the teams. The team with
the worst win-loss record was named on 11 of the cards,
the second-worst team on 10 cards, and so on, with the
team having the best record among the nonplayoff clubs
getting only one chance at having the first pick. The cards
were mixed, then drawn randomly to determine the order
in which the teams could draft players. Suppose there
are two exceptional players available in this year’s draft
and your favorite team had the third-worst record. Use a
simulation to find out how likely it is that your team gets
to pick first or second. Describe your simulation carefully.

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