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.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Think about what happens to teams that belong to both groups when 4 and 7 are added.
A student says there are 11 teams that are from the same division or have won more than 70% of their games because 4 + 7 = 11. What is the student's mistake?
The student should add the 2 overlapping teams again.The student counted the 2 teams in both groups twice and should subtract 2 once.The student should subtract all 4 same-division teams.The student should divide 11 by 2 because there are two groups.
Correct. The 2 teams in both groups are counted twice, so the overlap must be subtracted once.
Check how the 2 teams belonging to both groups are counted when the two group totals are added.
Next
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Hint
Remove the teams that belong to both groups from the 7 teams with winning records above 70%.
Of the 7 teams that had won more than 70% of their games, 2 were also from the same division. How many teams had won more than 70% of their games but were not from the same division?
Correct. There are 5 teams with winning records above 70% that are not from the same division.
Subtract the 2 teams in both groups from the 7 teams with winning records above 70%.
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Hint
Add the four non-overlapping categories and compare the total with the 12 remaining teams.
Suppose Tara checks the result another way. She counts 2 teams in both groups, 2 teams only from the same division, 5 teams only with winning records above 70%, and 3 teams in neither group. Which statement verifies that these categories correctly account for all 12 teams?
2 + 2 + 5 = 9, so the 3 teams in neither group should not be counted.2 + 5 + 3 = 10, so 2 teams must be missing.2 + 2 + 5 + 3 = 12, so every team is counted exactly once.4 + 7 + 3 = 14, so there must actually be 14 teams.
Correct. The four separate categories total 12, so they account for every team exactly once.
Use categories that do not overlap, then check whether their total equals 12.
Next
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Turnuva Kurası
TR
ARC_G09_DP_02_STORY_03
Turnuva Kurası
The Tournament Draw
EN
ARC_G09_DP_02_STORY_03
The Tournament Draw