Foundation June 2017 Paper 2 Q25
25 The table shows information about some CDs.
| Type | Rock | Pop | Jazz |
|---|---|---|---|
| Number of CDs | 2 | \(x\) | \(2x + 5\) |
A CD is chosen at random.
The probability it is rock is \(\dfrac{1}{20}\)
Work out the probability it is jazz. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| 40 | B1 | May be implied eg \(\dfrac{2}{40}\) |
| \(2 + x + 2x + 5 =\) their 40 or \(3x + 7 =\) their 40 or (their \(40 - 2 - 5) \div 3\) or \(33 \div 3\) | M1 | oe equation eg \(\;3x + 5 = 38\) (scores B1M1) their 40 must be an integer |
| \((x =)\ 11\) | A1ft | ft B0M1 Does not have to be an integer Accept answer rounded or truncated to at least 2 sf |
| \(\dfrac{27}{40}\) or 0.675 or 67.5% | B1ft | Only ft evaluation of \(\dfrac{2 \times \text{their integer } x + 5}{40}\) and \(0 \lt\) answer \(\lt 1\) Denominator must be 40 (may subsequently be simplified) |
| Alternative method 2 | ||
| \(\dfrac{2}{2 + x + 2x + 5} = \dfrac{1}{20}\) or \(\dfrac{x + 2x + 5}{2 + x + 2x + 5} = \dfrac{19}{20}\) | M2 | oe equation |
| \((x =)\ 11\) | A1 | |
| \(\dfrac{27}{40}\) or 0.675 or 67.5% | B1ft | Only ft evaluation of \(\dfrac{2 \times \text{their integer } x + 5}{40}\) and \(0 \lt\) answer \(\lt 1\) Denominator must be 40 (may subsequently be simplified) |
| Alternative method 3 | ||
| \(3x \to 100\% - 5\% - 12.5\%\) or \(3x \to 82.5\%\) | M1 | Using \(2 \to 5\%\) and \(5 \to 12.5\%\) oe |
| \(x \to 82.5\% \div 3\) or \(x \to 27.5\%\) | M1dep | oe |
| \(2x + 5 \to 2 \times 27.5\% + 12.5\%\) | M1dep | oe |
| \(\dfrac{27}{40}\) or 0.675 or 67.5% | A1 | |
| Alternative method 4 | ||
| \(3x \to 1 - \dfrac{1}{20} - \dfrac{2.5}{20}\) or \(3x \to \dfrac{16.5}{20}\) | M1 | Using \(2 \to \dfrac{1}{20}\) and \(5 \to \dfrac{2.5}{20}\) oe |
| \(x \to \dfrac{16.5}{20} \div 3\) or \(x \to \dfrac{5.5}{20}\) | M1dep | oe |
| \(2x + 5 \to 2 \times \dfrac{5.5}{20} + \dfrac{2.5}{20}\) or \(2x + 5 \to \dfrac{13.5}{20}\) | M1dep | oe |
| \(\dfrac{27}{40}\) or 0.675 or 67.5% | A1 | |
Additional guidance
| (Alt 1) \(\;x = 6\) (no working) \(\quad\) Answer \(\dfrac{17}{40}\) (first B1 implied) | B1M0A0B1ft |
| (Alt 1) \(\;2 + x + 2x + 5 = 20\) \(x = \dfrac{13}{3} \quad\) Answer \(\dfrac{13.666}{20}\) | B0M1A1ftB0ft |
| Answer \(\dfrac{13.5}{20}\) | B1M1A1B0 |
| 11 by inspection or T & I scores the first 3 marks | |
| Answer \(\dfrac{2x + 5}{40}\) | B1M0A0B0 |
| Answer \(\dfrac{2x + 5}{3x + 7}\) | Zero |
| Ratio eg 27 : 40 | B1M1A1B0 |
| Expressed only in words eg 27 out of 40 | B1M1A1B0 |
| 27 out of 40 and \(\dfrac{27}{40}\) | B1M1A1B1 |
| \(\dfrac{27}{40}\) seen with incorrect change of form or incorrect cancelling eg \(\dfrac{27}{40}\) and answer 0.27 | B1M1A1B1 |
| Ignore chance words if \(\dfrac{27}{40}\) seen eg \(\dfrac{27}{40}\) and answer Unlikely | B1M1A1B1 |