Hint
Use the stated units and precision. Multiply independent red probabilities with the original total unchanged.
Worked solution
(a)
Multiply independent red probabilities with the original total unchanged.
\(\displaystyle \frac{4}{9}\)×\(\displaystyle \frac{4}{9}\)=\(\displaystyle \frac{16}{81}\).
Answer: \(\displaystyle \frac{16}{81}\)
(b)
Multiply along the specified ordered branch.
\(\displaystyle \frac{4}{9}\)×\(\displaystyle \frac{5}{9}\)=\(\displaystyle \frac{20}{81}\).
Answer: \(\displaystyle \frac{20}{81}\)
(c)
Add both mutually exclusive one-red orders.
The disjoint RB and BR orders have equal probability, totalling \(\displaystyle \frac{40}{81}\).
Answer: \(\displaystyle \frac{40}{81}\)
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: Multiply independent red probabilities with the original total unchanged.
- 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: Multiply along the specified ordered branch.
- 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 both mutually exclusive one-red orders.
- 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.