Hint
Use the stated units and precision. Reduce both the red count and total after a first red selection.
Worked solution
(a)
Reduce both the red count and total after a first red selection.
Use \(\displaystyle \frac{1}{3}\)×\(\displaystyle \frac{3}{11}\)=\(\displaystyle \frac{1}{11}\).
Answer: \(\displaystyle \frac{1}{11}\)
(b)
Reduce the total but preserve the blue count after drawing red.
Use \(\displaystyle \frac{1}{3}\)×\(\displaystyle \frac{8}{11}\)=\(\displaystyle \frac{8}{33}\).
Answer: \(\displaystyle \frac{8}{33}\)
(c)
Add the two valid ordered outcomes.
RB and BR are disjoint and have the same product, giving \(\displaystyle \frac{16}{33}\).
Answer: \(\displaystyle \frac{16}{33}\)
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: Reduce both the red count and total after a first red selection.
- 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: Reduce the total but preserve the blue count after drawing red.
- 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: Add the two valid ordered outcomes.
- 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.