Higher November 2020 Paper 1R Q23
23 In a bag, there are only
3 blue beads
4 white beads
and \(x\) orange beads.
Jean is going to take at random two beads from the bag.
The probability that Jean will take two beads of the same colour is \(\dfrac{3}{8}\)
Find the total number of beads in the bag.
Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
e.g. \(\dfrac{3}{x + 7} \times \dfrac{2}{x + 6} + \dfrac{4}{x + 7} \times \dfrac{3}{x + 6} + \dfrac{x}{x + 7} \times \dfrac{x - 1}{x + 6}\left(= \dfrac{3}{8}\right)\) or e.g. \(\dfrac{3}{N} \times \dfrac{2}{N - 1} + \dfrac{4}{N} \times \dfrac{3}{N - 1} + \dfrac{N - 7}{N} \times \dfrac{N - 8}{N - 1}\left(= \dfrac{3}{8}\right)\) oe | M2 |
| \(5x^2 - 47x + 18 = 0\) oe (\(x = 9\)) or \(5N^2 - 117N + 592 = 0\) | M1 |
| Working required Answer: 16 | A1 |
| (4) | |
| (4 marks) |
Notes
M2: for all correct products and intention to add
(M1 for one correct product)
M1: Correct quadratic equation
A1: dep on M3