Stage 9 - Q1 - 3 marks
Design a random-digit simulation for red, blue and green with probabilities \(\frac{2}{10}\), \(\frac{2}{10}\) and \(\frac{6}{10}\). Use digits 0–9.
Hint
Each uniform random digit has probability one tenth.
Stage 9 - Q2 - 3 marks
Design 100 trials to estimate the probability of red from an opaque bag without changing its contents.
Hint
Keep the bag composition and selection process unchanged.
Stage 9 - Q3 - 3 marks
A fair-coin experiment has 100 heads after 200 tosses. The next toss is a head. Does the relative frequency move closer to \(\frac{1}{2}\)?
Hint
Compare both observed fractions with one half.
Stage 9 - Q4 - 3 marks
Run A gives 45 heads in 90 tosses; run B gives 227 in 450. Which is closer to \(\frac{1}{2}\)? Does this invalidate larger samples?
Hint
Separate what happened in these runs from the general tendency.
Stage 9 - Q5 - 3 marks
The table gives cumulative fair-coin results. Find all relative frequencies and describe the variation.
Hint
These are cumulative counts, so use the matching total trials for each row.
Stage 9 - Q6 - 3 marks
Design a random-digit simulation for red, blue and green with probabilities \(\frac{4}{10}\), \(\frac{3}{10}\) and \(\frac{3}{10}\). Use digits 0–9.
Hint
Each uniform random digit has probability one tenth.
Stage 9 - Q7 - 3 marks
Design 50 trials to estimate the probability of red from an opaque bag without changing its contents.
Hint
Keep the bag composition and selection process unchanged.
Stage 9 - Q8 - 3 marks
The table gives cumulative fair-coin results. Find all relative frequencies and describe the variation.
Hint
These are cumulative counts, so use the matching total trials for each row.
Stage 9 - Q9 - 3 marks
Run A gives 50 heads in 100 tosses; run B gives 252 in 500. Which is closer to \(\frac{1}{2}\)? Does this invalidate larger samples?
Hint
Separate what happened in these runs from the general tendency.
Stage 9 - Q10 - 5 marks
A fair-coin experiment gives 12 heads in 20 tosses. One more toss is made. Show that a head moves the relative frequency farther from \(\frac{1}{2}\), while a tail moves it closer.
Hint
Calculate the new fraction separately for each possible next outcome.