4MA0 Higher June 2017 Paper 3 Q20
20 A bag contains 12 marbles.
6 of the marbles are red, 4 of the marbles are blue and 2 of the marbles are green.
Raj takes at random 3 marbles from the bag.
Find the probability that exactly 2 of these marbles are blue.
(3)
| Scheme | Marks |
|---|---|
\(\dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{8}{10}\left(= \dfrac{96}{1320}\right)\) oe or \(\dfrac{4}{55}\) or \(\dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{6}{10}\left(= \dfrac{72}{1320}\right)\) and \(\dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{2}{10}\left(= \dfrac{24}{1320}\right)\) oe or \(3 \times \dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{6}{10}\left(= \dfrac{216}{1320}\right)\) oe or \(3 \times \dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{2}{10}\left(= \dfrac{72}{1320}\right)\) or | M1 |
\(3 \times \dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{8}{10}\) oe or \(3 \times \left(\dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{6}{10} + \dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{2}{10}\right)\) | M1 |
| \(\dfrac{288}{1320}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a complete method
A1: for \(\dfrac{288}{1320}\) oe e.g. \(\dfrac{12}{55}\)
accept 0.218(1818...) or 21.8(18…)%
rounded or truncated to at least 3SF
SC : with replacement (maximum 2 marks)
M1 for \(\dfrac{4}{12} \times \dfrac{4}{12} \times \dfrac{8}{12}\) oe or \(\dfrac{128}{1728}\) oe e.g. \(\dfrac{2}{27}\) or
\(\dfrac{4}{12} \times \dfrac{4}{12} \times \dfrac{6}{12}\) and \(\dfrac{4}{12} \times \dfrac{4}{12} \times \dfrac{2}{12}\) oe or
\(3 \times \dfrac{4}{12} \times \dfrac{4}{12} \times \dfrac{6}{12}\) or \(3 \times \dfrac{4}{12} \times \dfrac{4}{12} \times \dfrac{2}{12}\)
A1 for \(\dfrac{384}{1728}\) oe e.g. \(\dfrac{2}{9}\)