Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 25 students: 15 like maths, 12 like science, 6 like both. How many like maths ONLY?
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9.
2 A table row shows 12 and a row total of 30. What is the missing cell?
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18.
3 In a Venn diagram, which region should you fill in FIRST?
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The overlap (the "both" region).
Level 2 · Core
4 30 students: 18 soccer, 14 tennis, 7 both. How many play tennis ONLY?
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7.
5 Same group. How many play NEITHER sport?
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5.
6 Same group. What is P(both), as a fraction out of 30?
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7/30.
Level 3 · Challenge
7 20 like tea, 15 like coffee, 8 like both. How many like at least one?
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27.
8 30 students: 18 soccer, 14 tennis, 7 both. What is P(soccer or tennis)? Simplify.
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25/30 = 5/6.
9 You add two group totals and get 32, but the whole class is 30. What went wrong?
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The overlap was counted twice. Subtract it once: n(A or B) = n(A) + n(B) − n(both).