Stage 8 - Q1 - 2 marks
The larger-score game produces the pair (2, 5). What score is recorded?
Hint
Choose the larger entry.
Stage 8 - Q2 - 2 marks
The pair is (4, 4). What score is recorded?
Hint
Equal entries still have that common maximum.
Stage 8 - Q3 - 3 marks
Two spinners show 1, 2 and 3. List every ordered pair with maximum 2.
Hint
Keep the two orders distinct.
Stage 8 - Q4 - 3 marks
Two independent fair spinners show 1 to 3. Find the probability that the maximum is 3.
Hint
Do not count the pair (3,3) twice.
Stage 8 - Q5 - 3 marks
Two independent fair spinners show 1 to 5. Predict the frequency of maximum 4 in 100 trials.
Hint
Count the row and column for four while excluding larger entries.
Stage 8 - Q6 - 4 marks
Two independent fair spinners show 1 to 6. Find the probability that the maximum is at most 3.
Hint
The successful region is a square in the sample space.
Stage 8 - Q7 - 4 marks
Two independent fair spinners show 1 to 6. Find the probability that the maximum is at least 5.
Hint
Use a complementary square region.
Stage 8 - Q8 - 4 marks
A class records maxima 1 to 5 with frequencies 4, 13, 21, 26 and 36 in 100 trials. Compare its maximum-5 relative frequency with the theoretical value and state one limitation of the conclusion.
Hint
A matching experimental value is evidence, not proof.
Stage 8 - Q9 - 5 marks
Two independent fair spinners show 1 to 5. Which is more likely: maximum exactly 4, or maximum at most 3? Explain using counts.
Hint
Compare a border with a square, rather than comparing the target numbers.
Stage 8 - Q10 - 6 marks
For two independent fair spinners showing 1 to \(n\), derive a rule for the probability that the maximum is exactly \(k\). Verify that the resulting counts add to \(n^2\).
Hint
Think of building an n by n square from successive L-shaped borders.