4400 Higher November 2004 Paper 3 Q20
20 A box contains 7 good apples and 3 bad apples.
Nick takes two apples at random from the box, without replacement.
(a)
(i) Calculate the probability that both of Nick’s apples are bad.
(ii) Calculate the probability that at least one of Nick’s apples is good. (4)
Another box contains 8 good oranges and 4 bad oranges.
Crystal keeps taking oranges at random from the box one at a time, without replacement, until she gets a good orange.
(b) Calculate the probability that she takes exactly three oranges. (2)
| Scheme | Marks |
|---|---|
| (i) \(\frac{3}{10} \times \frac{2}{9}\) | M1 |
| \(\frac{1}{15}\) or 0.066(66..) oe | A1 |
| (ii) 1 − her \(\frac{1}{15}\) | M1 |
| \(\frac{14}{15}\) oe | A1ft |
| (4) |
| Scheme | Marks |
|---|---|
| \(\frac{4}{12} \times \frac{3}{11} \times \frac{8}{10}\) | M1 |
| \(\frac{4}{55}\) or 0.072(72..) oe | A1 |
| (2) | |
| (6 marks) |