Foundation November 2022 Paper 1 Q16
16 Bag A and bag B each contain only red discs and green discs.
| Bag A | Contains 28 red discs There are twice as many red discs as green discs |
|---|---|
| Bag B | Contains 20 green discs There are 3 red discs for every 5 green discs |
(a) Work out the total number of discs. [3 marks]
(b) A different bag, C, is empty.
The 28 red discs from A are put into C.
The 20 green discs from B are also put into C.
One disc is now picked at random from each bag.
Complete each statement. [3 marks]
The probability of red from A is \(\ldots\ldots\)
The probability of red from B is \(\ldots\ldots\)
The probability of red from C is \(\ldots\ldots\)
| Answer | Mark | Comments |
|---|---|---|
| (green in A =) \(28 \div 2\) or 14 or (red in B =) \(20 \div 5 \times 3\) or 12 or (total in A =) \(28 \times \dfrac{3}{2}\) or (total in B =) \(20 \times \dfrac{8}{5}\) | M1 | oe |
| 14 and 12 or (total in A =) 42 or (total in B =) 32 or (total green =) 34 or (total red =) 40 | A1 | may be implied by final answer |
| 74 | A1 | SC2 116 (using 56 green discs in A) or 26 (green in A + red in B) |
Additional guidance
| \(14 + 28 + 15 = 57\) (implied correct interim total for Bag A) \(14 + 28 + 15 + 20 = 77\) (implied correct interim total for Bag A) 14 and 15, with 77 on answer line (implied correct interim total for Bag A) | M1A1A0 M1A1A0 M1A1A0 |
| \(14 + 28 + 15 + 20\), no answer (no implied correct interim total) | M1A0A0 |
| Answer | Mark | Comments |
|---|---|---|
| 0 | B1 | oe fraction decimal or percentage |
| 1 | B1 | oe fraction decimal or percentage |
| \(\dfrac{28}{48}\) or \(\dfrac{14}{24}\) or \(\dfrac{7}{12}\) or 0.58(3…) | B1 | oe fraction decimal or percentage |
Additional guidance
| Ignore incorrect simplification after correct answer seen | |
| Do not accept probabilities written as ratios | |
| First B1 \(\dfrac{0}{14}\) (denominator may be any value except 0) First B1 \(\dfrac{0}{0}\) | B1 B0 |
| Second B1 \(\dfrac{12}{12}\) | B1 |
| Do not allow if only words given eg First answer Impossible Second answer Certain | B0B0 |
| Penalise only the first occurrence of “out of” eg 0 out of 48, 48 out of 48, 28 out of 48 eg 0, 1, 28 out of 48 | B0B1B1 B1B1B0 |
| Penalise only the first occurrence of an incorrect but consistent denominator eg \(\dfrac{0}{74}\), \(\dfrac{12}{74}\), \(\dfrac{28}{74}\) eg 0, \(\dfrac{12}{116}\), \(\dfrac{28}{74}\) | B1B0B1 B1B0B0 |