Higher June 2017 Paper 2 Q5
5 A code has 4 digits.
Each digit is a number from 0 to 9
Digits may be repeated.
The code starts \(\quad 5 \;\; 4 \;\; 1\)
| 5 | 4 | 1 |
(a) Amy knows the last digit is odd but not 7
She chooses a different odd number at random.
What is the probability that she chooses the correct number? [1 mark]
(b) The 4-digit code is changed to an even number.
The first digit is 3
How many possible codes are there? [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{4}\) or 0.25 or 25% | B1 | oe |
Additional guidance
| Ratio eg 1 : 4 or 1 : 3 | B0 |
| \(\dfrac{1}{4}\) seen and answer 1 : 4 | B1 |
| Expressed only in words eg 1 out of 4 | B0 |
| 1 out of 4 and \(\dfrac{1}{4}\) | B1 |
| \(\dfrac{1}{4}\) seen with change to incorrect decimal or incorrect percentage eg \(\dfrac{1}{4}\) and answer 0.4 | B1 |
| Ignore chance words if \(\dfrac{1}{4}\) seen eg \(\dfrac{1}{4}\) and answer Likely | B1 |
| Answer | Mark | Comments |
|---|---|---|
| \((1 \times)\ 10\ (\times)\ 10\ (\times)\ 5\) or \(\dfrac{10 \times 10 \times 10}{2}\) or \(\dfrac{1000}{2}\) | M1 | oe |
| 500 | A1 | SC1 5 or 324 or 400 or 405 |
Additional guidance
| \(10 + 10 + 5\) | M0A0 |
| SCs are for the answers from not including zero at least once ie \(9 \times 9 \times 4\) or \(10 \times 10 \times 4\) or \(9 \times 9 \times 5\) or from a misread ie \(1 \times 1 \times 1 \times 5\) |