Stage 9 - Q1 - 2 marks
An event occurs 8 times in 50 trials. Find its relative frequency.
Hint
Keep the event count in the numerator.
Stage 9 - Q2 - 3 marks
A spinner lands on gold 19 times in 40 spins. Use these results to predict gold in 160 future spins. Is the prediction guaranteed?
Hint
The observed fraction is an estimate for future trials.
Stage 9 - Q3 - 2 marks
After 120 trials there are 96 successes; after 140, there are 104. Find the relative frequency in the final 20 trials.
Hint
The final cumulative count includes the earlier successes.
Stage 9 - Q4 - 3 marks
Run A has 11 successes in 110 trials; run B has 25 successes in 220 trials. Find the combined relative frequency.
Hint
Unequal-sized runs must not receive equal weights.
Stage 9 - Q5 - 2 marks
A bag has 40 counters. In 400 draws with replacement and mixing, 260 are red. Estimate the number of red counters.
Hint
Multiply the estimated probability by the bag size.
Stage 9 - Q6 - 3 marks
A fair 7-sector spinner has one gold sector. In 210 spins gold occurs 31 times. Compare relative frequency with theory.
Hint
Calculate each probability separately, then compare.
Stage 9 - Q7 - 3 marks
Run A has 62 successes in 80 trials; run B has 127 successes in 160 trials. Find the combined relative frequency.
Hint
Unequal-sized runs must not receive equal weights.
Stage 9 - Q8 - 2 marks
After 70 trials there are 15 successes; after 90, there are 28. Find the relative frequency in the final 20 trials.
Hint
The final cumulative count includes the earlier successes.
Stage 9 - Q9 - 3 marks
A fair 3-sector spinner has one gold sector. In 90 spins gold occurs 28 times. Compare relative frequency with theory.
Hint
Calculate each probability separately, then compare.
Stage 9 - Q10 - 5 marks
An event occurs 18 times in 40 trials. After a second run of 60 trials, the combined relative frequency is 0.37. Find the second-run count and relative frequency.
Hint
Recover the combined number of successes first.