Stage 8 - Q1 - 2 marks
A coin is tossed and a spinner labelled A, B, C is spun. How many ordered outcomes are possible?
Hint
Pair heads and tails with each letter.
Stage 8 - Q2 - 2 marks
One card is chosen from X, Y and one from 1, 2, 3, 4. List the eight ordered outcomes.
Hint
Use two rows, one for each letter.
Stage 8 - Q3 - 2 marks
Fair independent spinners show 1, 3 and 2, 4. List the four possible totals.
Hint
A repeated total is still produced by a distinct pair.
Stage 8 - Q4 - 2 marks
Fair independent spinners show 1, 3 and 2, 4. Find the probability of a total of five.
Hint
Count ordered pairs, not different totals.
Stage 8 - Q5 - 3 marks
Fair independent spinners show 1, 2, 4 and 1, 3. Find the probability that the product is even.
Hint
Use the parity of the factors.
Stage 8 - Q6 - 3 marks
Two fair dice are rolled. Find the probability that their total is at most four.
Hint
List the small totals systematically.
Stage 8 - Q7 - 4 marks
Two fair independent spinners show 1 to 4. Find the probability of different scores, using a complement.
Hint
Matching pairs form a simple diagonal in the table.
Stage 8 - Q8 - 4 marks
A game uses two fair dice. A player wins on a total of 6 or 8. Predict the number of wins in 180 games. Is your prediction guaranteed?
Hint
Count both winning totals before scaling.
Stage 8 - Q9 - 5 marks
Two fair spinners each show 1 to 5. Player A wins if the first score is larger, B if the second is larger, and ties score nothing. Are A and B equally likely to win? Is either winning probability \(\frac12\)?
Hint
Separate equality from the two strict inequalities.
Stage 8 - Q10 - 6 marks
Two fair spinners each show 1 to 4. Design a winning rule based only on the total that gives probability \(\frac12\). Give one rule and justify it with the whole sample space.
Hint
Try grouping totals by parity.