1MA0 Higher June 2015 Paper 1 Q19
19 There are \(n\) sweets in a bag.
6 of the sweets are orange.
The rest of the sweets are yellow.
Hannah takes at random a sweet from the bag.
She eats the sweet.
Hannah then takes at random another sweet from the bag.
She eats the sweet.
The probability that Hannah eats two orange sweets is \(\dfrac{1}{3}\)
(a) Show that \(n^2 - n - 90 = 0\) (3)
(b) Solve \(n^2 - n - 90 = 0\) to find the value of \(n\). (3)
| Answer | Mark | Notes |
|---|---|---|
| Proof | 3 | M1 for \(\dfrac{6}{n}\) or \(\dfrac{5}{n - 1}\) M1 for \(\dfrac{6}{n} \times \dfrac{5}{n - 1} \left(= \dfrac{1}{3}\right)\) A1 for fully correct algebra leading to \(n^2 - n - 90 = 0\) |
| Answer | Mark | Notes |
|---|---|---|
| 10 | 3 | M1 for correct start to a solution, eg. \((n \pm 10)(n \pm 9)\) or substitution into the quadratic formula, condoning one sign error or \((n - 0.5)^2 - 0.25 - 90\) A1 for \((n - 10)(n + 9)\) or for 10 and \(-9\) or \(\tfrac{1 \mp 19}{2}\) oe A1 for 10 only |