4MA0 Higher January 2015 Paper 3 Q16
16 Gemma has 9 counters.
Each counter has a number on it.
Gemma puts the 9 counters into a bag.
She takes at random a counter from the bag and does not replace the counter.
She then takes at random a second counter from the bag.
(a) Work out the probability that the number on each counter is an even number. (2)
(b) Work out the probability that the number on the first counter added to the number on the second counter gives an odd number. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{4}{9} \times \dfrac{3}{8}\) | M1 |
| \(\dfrac{1}{6}\) | A1 |
| (2) |
Notes
A1: oe, eg \(\dfrac{12}{72}\)
Allow 0.16(666...) rounded or truncated to at least 2dp
| Scheme | Marks |
|---|---|
\(\dfrac{5}{9} \times \dfrac{4}{8} + \dfrac{4}{9} \times \dfrac{5}{8}\) or \(\dfrac{20}{72} + \dfrac{20}{72}\) oe or \(1 - \dfrac{4}{9} \times \dfrac{3}{8} - \dfrac{5}{9} \times \dfrac{4}{8}\) or \(1 - \dfrac{\text{“}1\text{”}}{6} - \dfrac{5}{9} \times \dfrac{4}{8}\) oe | M2 |
| \(\dfrac{5}{9}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M2: M1 for \(\dfrac{4}{9} \times \dfrac{5}{8}\) or \(\dfrac{5}{9} \times \dfrac{4}{8}\) or \(\dfrac{20}{72}\) oe
Accept fractions evaluated \(\dfrac{20}{72} = 0.27\dot{7}\), \(\dfrac{12}{72} = 0.16\dot{6}\) rounded or truncated to at least 2dp.
A1: oe, eg \(\dfrac{40}{72}\) or \(\dfrac{20}{36}\)
Allow 0.55(5555....) rounded or truncated to at least 2dp
Alternative: with replacement
| Scheme | Marks |
|---|---|
| \(\dfrac{5}{9} \times \dfrac{4}{9} + \dfrac{4}{9} \times \dfrac{5}{9}\) or \(\dfrac{40}{81}\) oe | M2 |
Notes
M2: M1 for \(\dfrac{5}{9} \times \dfrac{4}{9}\) or \(\dfrac{4}{9} \times \dfrac{5}{9}\) or \(\dfrac{20}{81}\) oe
Accept fractions evaluated
\(\dfrac{20}{81} = 0.24(691358\ldots)\)
\(\dfrac{40}{81} = 0.49(382716\ldots)\)
rounded or truncated to at least 2dp