Hint
Use the stated units and precision. Use the Club A row as the conditional sample space.
Worked solution
(a)
Use the Club A row as the conditional sample space.
Restrict to the 13 Club A members; 6 walk. The fraction is \(\displaystyle \frac{6}{13}\).
Answer: \(\displaystyle \frac{6}{13}\)
(b)
Use the walking column rather than reversing the earlier conditional fraction.
Restrict to the 11 walkers; 6 are in A, giving \(\displaystyle \frac{6}{11}\).
Answer: \(\displaystyle \frac{6}{11}\)
(c)
Restrict to the Club B row.
Among 12 Club B members, 7 take the bus, giving \(\displaystyle \frac{7}{12}\).
Answer: \(\displaystyle \frac{7}{12}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Use the Club A row as the conditional sample space.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the walking column rather than reversing the earlier conditional fraction.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Restrict to the Club B row.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.