Higher November 2019 Paper 3 Q8
8 In a choir there are 35 men and 48 women.
The probability that a man chosen at random wears glasses is \(\dfrac{2}{5}\)
The probability that a woman chosen at random wears glasses is \(\dfrac{3}{8}\)
(a) Work out the number of people in the choir who wear glasses. [3 marks]
(b) A person is chosen at random from the choir.
Work out the probability that the person does not wear glasses. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{2}{5} \times 35\) or \(\dfrac{3}{8} \times 48\) | M1 | oe |
| 14 or 18 | A1 | |
| 32 | A1 |
Additional guidance
| Do not ignore further working after 32 seen | |
| \(\dfrac{32}{83}\) on answer line | M1A1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(35 + 48 -\) their 32 or \(35 -\) their \(14 + 48 -\) their 18 or 51 | M1 | oe their 32 from (a) their 14 and their 18 from (a) |
| \(\dfrac{51}{83}\) or 0.61(4…) or 61(.4…)% | A1ft | ft their 32 from (a) |
| Alternative method 2 | ||
| \(\left(1 - \dfrac{2}{5}\right) \times 35 + \left(1 - \dfrac{3}{8}\right) \times 48\) or \(\dfrac{3}{5} \times 35 + \dfrac{5}{8} \times 48\) or \(21 + 30\) | M1 | oe |
| \(\dfrac{51}{83}\) or 0.61(4…) or 61(.4…)% | A1 | |
Additional guidance
Ignore incorrect conversion if correct fraction seen
If their answer in part (a) is a fraction, only allow follow through if their numerator is used in part (b)
Alt 1 ft decimal or percentage answers accept rounding to at least 2 sf