Higher January 2022 Paper 1R Q13
13 Hector has a bag that contains 12 counters.
There are 7 green counters and 5 red counters in the bag.
Hector takes at random a counter from the bag.
He looks at the counter and puts the counter back into the bag.
Hector then takes at random a second counter from the bag.
He looks at the counter and puts the counter back into the bag.
Meghan has a jar containing 15 counters.
There are only blue counters, green counters and red counters in the jar.
Hector is going to take at random one of the counters from his bag of 12 counters.
He will look at the counter and put the counter back into the bag.
Hector is then going to take at random a second counter from his bag.
He will look at the counter and put the counter back into the bag.
Meghan is then going to take at random one of the counters from her jar of counters.
She will look at the counter and put the counter back into the jar.
The probability that the 3 counters each have a different colour is \(\dfrac{7}{24}\)
| Scheme | Marks |
|---|---|
| \(\dfrac{5}{12}\) | B1 |
| \(\dfrac{7}{12}\), \(\dfrac{5}{12}\) | B1 |
| (2) |
Notes
B1: for first choice correct
0.41(666…) to 2 dp truncated or rounded
B1: for second choice correct
0.58(333…) to 2 dp truncated or rounded
0.41(666…) to 2 dp truncated or rounded
| Scheme | Marks |
|---|---|
| \(\text{``}\dfrac{5}{12}\text{''} \times \dfrac{5}{12}\) oe | M1 |
| \(\dfrac{25}{144}\) | A1 |
| (2) |
Notes
M1: ft from their tree diagram
0.58(333…) to 2 dp truncated or rounded
A1: oe 0.17(361111…) to 2 dp truncated or rounded or
17.(361111)% to 2 sf truncated or rounded
| Scheme | Marks |
|---|---|
\(\dfrac{7}{12} \times \dfrac{5}{12} \times \dfrac{x}{15}\) oe or \(\dfrac{7}{12} \times \dfrac{5}{12} \times y\) or \(2 \times \dfrac{7}{12} \times \dfrac{5}{12}\) oe | M1 |
\(2 \times \dfrac{7}{12} \times \dfrac{5}{12} \times \dfrac{x}{15} = \dfrac{7}{24}\) oe or \(2 \times \dfrac{7}{12} \times \dfrac{5}{12} \times y = \dfrac{7}{24}\) oe or \(\dfrac{\frac{7}{24}}{2 \times \frac{7}{12} \times \frac{5}{12}}\left(= \dfrac{3}{5}\right)\) oe | M1 |
| 9 | A1 |
| (3) | |
| (7 marks) |
Notes
M1: for \(GRB\) or \(RGB\) or
\(2 \times GR\) or \(2 \times RG\)
M1: (ft their tree diagram) for a complete method
0.29(166…) to 2 dp truncated or rounded