Foundation June 2017 Paper 3 Q25
25 There are 720 boys and 700 girls in a school.
The probability that a boy chosen at random studies French is \(\dfrac{2}{3}\)
The probability that a girl chosen at random studies French is \(\dfrac{3}{5}\)
(a) Work out the number of students in the school who study French. [3 marks]
(b) Work out the probability that a student chosen at random from the whole school does not study French. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{2}{3} \times 720\) or \(\dfrac{3}{5} \times 700\) | M1 | oe Accept use of 0.66… or 0.67 |
| 480 or 420 | A1 | |
| 900 | A1 | Ignore fw |
Additional guidance
| 900 with no working | M1A1A1 |
| 900 out of 1420 or \(\dfrac{900}{1420}\) (ignore fw) | M1A1A1 |
| \(\dfrac{480}{720}\) (480 boys out of 720) or \(\dfrac{420}{1420}\) (420 girls out of 1420 students) | M1A1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(720 + 700\) or 1420 or \(720 + 700 -\) their 900 or 520 | M1 | oe |
| \(\dfrac{520}{1420}\) or \(\dfrac{26}{71}\) | A1ft | oe fraction, decimal or percentage 0.36(6…) or 0.37 36.(6…)% or 37% ft their part (a) Ignore fw |
| Alternative method 2 | ||
| \(720 + 700\) or 1420 or \(\dfrac{1}{3} \times 720\) or 240 or \(\dfrac{2}{5} \times 700\) or 280 or \(240 + 280\) or 520 | M1 | oe |
| \(\dfrac{520}{1420}\) or \(\dfrac{26}{71}\) | A1 | oe fraction, decimal or percentage 0.36(6…) or 0.37 36.(6…)% or 37% Ignore fw |
| Alternative method 3 | ||
| \(720 + 700\) or 1420 or \(\dfrac{900}{1420}\) or \(\dfrac{45}{71}\) or \(\dfrac{\text{their } 900}{1420}\) | M1 | oe fraction, decimal or percentage 0.63… or 0.63 63.(…)% or 63% |
| \(\dfrac{520}{1420}\) or \(\dfrac{26}{71}\) | A1ft | oe fraction, decimal or percentage 0.36(6…) or 0.37 36.(6…)% or 37% ft their part (a) Ignore fw |
Additional guidance
| \(\dfrac{520}{1420}\) followed by incorrect simplification of fraction | M1A1 |