4MA0 Higher June 2017 Paper 4R Q16
16 Here are six cards.
Each card has a number on it.
| 1 | 3 | 3 | 3 | 4 | 4 |
The cards are turned over to hide their numbers and are then mixed up.
Malachi takes at random two of the cards and turns them over to show their numbers.
(a) Calculate the probability that the number 4 is on both of the cards Malachi takes. (2)
(b) Calculate the probability that the sum of the numbers on the two cards Malachi takes is an even number. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{6} \times \dfrac{1}{5}\) oe | M1 |
| \(\dfrac{1}{15}\) | A1 |
| (2) |
Notes
M1: For a complete method
A1: oe
Eg \(\dfrac{2}{30}\)
Accept 0.066(666...) rounded or truncated to at least 3 decimal places
| Scheme | Marks |
|---|---|
\(\dfrac{4}{6} \times \dfrac{3}{5}\) or 0.4 or \(\dfrac{2}{6} \times \dfrac{1}{5}\) or 0.066(666...) or \(\dfrac{1}{6} \times \dfrac{3}{5}\) or \(\dfrac{3}{6} \times \dfrac{1}{5}\) or 0.1 or \(\dfrac{3}{6} \times \dfrac{2}{5}\) or 0.2 or \(\dfrac{2}{6} \times \dfrac{1}{5}\) or 0.066(666...) | M1 |
\(\dfrac{4}{6} \times \dfrac{3}{5} + \dfrac{2}{6} \times \dfrac{1}{5}\) or \(\dfrac{1}{6} \times \dfrac{3}{5} + \dfrac{3}{6} \times \dfrac{1}{5} + \dfrac{3}{6} \times \dfrac{2}{5} + \dfrac{2}{6} \times \dfrac{1}{5}\) | M1 |
| \(\dfrac{7}{15}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: One correct product that gives an even number
M1: Sum of correct products
A1: oe
Accept 0.466(666...) rounded or truncated to at least 3 decimal places
With Replacement
| Scheme | Marks |
|---|---|
\(\dfrac{4}{6} \times \dfrac{4}{6}\) or 0.444(444) or \(\dfrac{2}{6} \times \dfrac{2}{6}\) or 0.111(111...) or \(\dfrac{1}{6} \times \dfrac{3}{6}\) or \(\dfrac{3}{6} \times \dfrac{1}{6}\) or 0.083(333...) or \(\dfrac{2}{6} \times \dfrac{2}{6}\) or 0.111(111...) or \(\dfrac{3}{6} \times \dfrac{3}{6}\) or 0.25 or \(\dfrac{1}{6} \times \dfrac{1}{6}\) or 0.027(777...) | M1 |
\(\dfrac{4}{6} \times \dfrac{4}{6} + \dfrac{2}{6} \times \dfrac{2}{6}\) oe or \(\dfrac{1}{6} \times \dfrac{3}{6} + \dfrac{3}{6} \times \dfrac{1}{6} + \dfrac{2}{6} \times \dfrac{2}{6} + \dfrac{3}{6} \times \dfrac{3}{6} + \dfrac{1}{6} \times \dfrac{1}{6}\) oe or or \(\dfrac{5}{9}\) or 0.555(555...) | M1 |
Alternative method
| Scheme | Marks |
|---|---|
| \(1 - \left(\dfrac{2}{6} \times \dfrac{4}{5} + \dfrac{4}{6} \times \dfrac{2}{5}\right)\) oe | M2 |
| \(\dfrac{7}{15}\) | A1 |
Notes
A1: oe
Accept 0.466(666...) rounded or truncated to at least 3 decimal places