Higher June 2024 Paper 1R Q21
21 There are 25 counters in a bag such that
6 counters are blue
\(x\) counters are orange, where \(x \gt 9\)
the rest of the counters are pink
Maalam takes at random two of the counters from the bag.
The probability that Maalam takes one orange counter and one pink counter is \(\dfrac{22}{75}\)
Calculate the probability that Maalam takes 2 pink counters from the bag.
Show clear algebraic working.
(5)
| Scheme | Marks |
|---|---|
| eg \(\dfrac{x}{25} \times \dfrac{25 - (x + 6)}{24}\) or \(\dfrac{x}{25} \times \dfrac{19 - x}{24}\) oe | M1 |
| eg \(2 \times \left(\dfrac{x}{25} \times \dfrac{19 - x}{24}\right) = \dfrac{22}{75}\) oe | M1 |
| eg \(2x^2 - 38x + 176 (= 0)\) oe eg \(x^2 - 19x + 88 (= 0)\) | M1 |
| \(x = 11\) or pink = 25 – 6 – 11 (= 8) | M1 |
Working required Answer: \(\dfrac{7}{75}\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for a correct product for P(orange , pink)
M1: for setting up a correct equation in \(x\)
M1: for dealing with the fractions to set up a correct quadratic equation
M1: (dep on M1)
for \(x = 11\) or pink = 25 – 6 – 11 (= 8)
A1: (dep on M2) oe eg 0.093... or 9.3...%