Stage 8 - Q1 - 2 marks
A coin lands heads 18 times in 40 tosses. Estimate the probability of heads.
Hint
Use successes divided by trials.
Stage 8 - Q2 - 2 marks
A spinner lands on green 12 times in 50 spins. Estimate the probability of not green.
Hint
Count the complementary outcomes.
Stage 8 - Q3 - 2 marks
A machine makes 7 imperfect items in a test of 140. Using this estimate, predict the imperfect count in 600 items.
Hint
Use the observed fraction, assuming the process stays the same.
Stage 8 - Q4 - 3 marks
A fair die gives a six 9 times in 48 rolls. Compare the observed relative frequency with the theoretical probability.
Hint
The theoretical denominator counts die faces; the experimental denominator counts rolls.
Stage 8 - Q5 - 3 marks
Two groups record 11 red results in 30 spins and 24 red results in 70 spins. Find the pooled red estimate.
Hint
Treat the experiments as one data set.
Stage 8 - Q6 - 4 marks
A pupil averages \(\frac12\) from 10 trials and \(\frac15\) from 100 trials to estimate \(\frac7{20}\). Find the correct combined estimate and explain the error.
Hint
Recover the event counts before combining.
Stage 8 - Q7 - 4 marks
A fair coin lands heads eight times in a row. A pupil says tails must be more likely next. Evaluate the claim.
Hint
Distinguish independence from a tendency to balance out over many trials.
Stage 8 - Q8 - 4 marks
A class tests a spinner only when it is held on a tilted desk, while another class uses a flat desk. Should their data be pooled to estimate the flat-desk probability? Explain a better plan.
Hint
Ask whether both groups model the same random process.
Stage 8 - Q9 - 5 marks
A coin has produced 32 heads in 80 tosses. How many heads in the next 20 tosses would make the overall observed heads frequency exactly \(\frac12\)? Is that outcome guaranteed for a fair coin?
Hint
Work backwards from the required final head count.
Stage 8 - Q10 - 6 marks
An event occurs in \(\frac14\) of the first 40 trials. After 60 further trials the pooled relative frequency is \(\frac25\). Find its frequency in the second experiment, then explain why the two relative frequencies can differ even if conditions are unchanged.
Hint
Translate each fraction into a count using its own number of trials.