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 A die was rolled 50 times and gave a 6 nine times. What is the relative frequency of a 6? (as a decimal)
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0.18.
2 How many heads would you expect in 80 tosses of a fair coin?
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40.
3 What goes on the bottom of a relative frequency fraction — trials or outcomes?
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The number of trials.
Level 2 · Core
4 A coin tossed 60 times gave 33 heads. Find the relative frequency. (as a decimal)
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0.55.
5 How many sixes would you expect in 300 rolls of a fair die?
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50.
6 How many hearts would you expect in 40 draws from a full deck, replacing each card?
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10.
Level 3 · Challenge
7 A die rolled 600 times gives face 6 a total of 147 times. How many were expected?
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100 — so 147 suggests bias towards 6.
8 Which gives better evidence that a die is loaded: 12 rolls or 600 rolls?
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600 rolls — small samples stray far from the theory by chance alone.
9 A coin gives 46 heads in 100 tosses. Is there evidence of bias?
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No — 46 against an expected 50 is normal variation.