Foundation November 2023 Paper 2 Q18
18 A box contains 36 chocolates.
The chocolates are milk or dark and have hard or soft centres.
\(\dfrac{4}{9}\) of the chocolates have soft centres.
There are twice as many milk chocolates as dark.
5 of the dark chocolates have soft centres.
| Hard centre | Soft centre | |
|---|---|---|
| Milk | ||
| Dark | 5 |
One chocolate is chosen at random.
| Answer | Mark | Comments | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(36 \times \dfrac{4}{9}\) or 16 (Soft) or \(36 \times \dfrac{5}{9}\) or 20 (Hard) or \(36 \times \dfrac{1}{3}\) or 12 (Dark) or \(36 \times \dfrac{2}{3}\) or 24 (Milk) | M1 | oe implied by the numbers in the relevant row or column making the correct total accept 16 seen in Milk Soft accept 12 in Dark Hard | |||||||||
| A3 | A2 two of Milk Soft \(= 11\), Dark Hard \(= 7\) and Milk Hard \(= 13\) A1 Milk Soft \(= 11\) or Dark Hard \(= 7\) |
Additional guidance
| M1A2 | |||||||||
| M1A1 | |||||||||
For M1 the values must be seen outside the table or implied by the table but also accept 16 seen in Milk Soft or 12 in Dark Hard
| M1 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{5}{36}\) or \(0.13\dot{8}\) or \(13.\dot{8}\%\) | B1 | oe fraction, decimal or percentage accept rounding to 2 sf or better |
Additional guidance
Ignore incorrect simplification or conversion attempt to fraction, decimal or percentage (but not ratio) after correct probability seen
Do not allow eg 5 in 36 or 5 out of 36 unless the correct probability seen
Do not allow ratio
Ignore words if correct probability seen
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{\text{their } 20}{36}\) or \(\dfrac{5}{9}\) or \(0.\dot{5}\) or \(55.\dot{5}\%\) | B1ft | oe fraction, decimal or percentage correct or ft their Hard total from the table accept rounding to 2 sf or better |
Additional guidance
Ignore incorrect simplification or conversion attempt to fraction, decimal or percentage (but not ratio) after correct probability seen
Do not allow eg 20 in 36 or 20 out of 36 unless the correct probability seen
Do not allow ratio
Ignore words if correct probability seen