4400 Higher June 2008 Paper 3 Q16
16 Here are 9 cards.
Each card has a number on it.
| 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 |
Lee takes a card at random.
He records the number which is on the card and replaces the card.
He then takes a second card at random and records the number which is on the card.
(a) Calculate the probability that he will take two even numbers. (2)
(b) Calculate the probability that he will take two numbers with a sum of 43 (3)
| Scheme | Marks |
|---|---|
| \(\frac{5}{9} \times \frac{5}{9}\) | M1 |
| \(\frac{25}{81}\) | A1 |
| (2) |
Notes
M1: for \(\frac{5}{9} \times \frac{5}{9}\)
A1: for \(\frac{25}{81}\) or 0.31 or better
Sample space method - award 2 marks for a correct answer, otherwise no marks
| Scheme | Marks |
|---|---|
| \(\frac{1}{9} \times \frac{1}{9}\) or \(\frac{1}{81}\) | M1 |
| \(\frac{1}{9} \times \frac{1}{9} \times 4\) oe | M1 |
| \(\frac{4}{81}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for \(\frac{1}{9} \times \frac{1}{9}\) or \(\frac{1}{81}\)
M1: for \(\frac{1}{9} \times \frac{1}{9} \times 4\) oe
A1: for \(\frac{4}{81}\) or 0.05 or better
SC
M1 for \(\frac{1}{9} \times \frac{1}{8}\) or \(\frac{1}{72}\)
M1 for \(\frac{1}{9} \times \frac{1}{8} \times 4\) oe
Sample space method - award 3 marks for a correct answer, otherwise no marks