Foundation January 2023 Paper 2R Q20
20 In a bag, there are only red counters, blue counters, green counters and yellow counters.
The total number of counters in the bag is 80
In the bag
the number of red counters is \(x + 7\)
the number of blue counters is \(x - 11\)
the number of green counters is \(3x\)
Jude takes at random a counter from the bag.
The probability that he takes a red counter is \(\dfrac{1}{4}\)
Work out the probability that Jude takes a yellow counter.
(4)
| Scheme | Marks |
|---|---|
| eg \(\dfrac{x + 7}{80} = \dfrac{1}{4}\) or \(4(x + 7) = 80\) or \(x + 7 = 20\) | M1 |
eg \(x = 80 \times \dfrac{1}{4} - 7\;(= 13)\) or \(4x + 28 = 80\) and \(x = \dfrac{80 - 28}{4}\;(= 13)\) or \(x = 13\) | M1 |
eg \(80 - (\text{“}13\text{”} + 7 + \text{“}13\text{”} - 11 + 3 \times \text{“}13\text{”})\;(= 19)\) or \(\dfrac{\text{“}13\text{”} + 7 + \text{“}13\text{”} - 11 + 3 \times \text{“}13\text{”}}{80}\left(= \dfrac{61}{80}\right)\) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{19}{80}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for setting up a correct equation in terms of \(x\) only
M1: for a complete method to find the value of \(x\) or \(x = 13\). Award of this mark implies M2.
M1: for a method to find the number of yellow counters or P(R or B or G)
A1: oe eg accept 0.2375 or 23.75% or 0.237 or 23.7% or 0.238 or 23.8% or 0.24 or 24%