Emek and Tara's basketball team had advanced to the next tournament round, where one of 12 remaining teams would be selected randomly as their opponent. Four teams were from the same division as Emek and Tara's team, while 7 had won more than 70% of their games. Two teams belonged to both groups. Emek and Tara wanted to know how likely they were to face an opponent with at least one of these characteristics. They first added 4 and 7, but Tara noticed that the 2 teams belonging to both groups had been counted twice. Subtracting the overlap gave 4 + 7 - 2 = 9 teams. Therefore, the probability of drawing a team from the same division or one with a winning record above 70% was 9/12, or 75%. They also noted that only 3 teams belonged to neither group. Since the draw was more likely to produce one of the 9 relevant opponents, the team focused its practice on strategies for those matchups. When practice ended, they felt prepared for the possibilities the draw was most likely to bring.




