4400 Higher June 2006 Paper 4 Q16
16 The sides of a fair six-sided dice are numbered from 1 to 6
The dice is thrown three times.
Find the probability that it shows a 1 at least twice.
(4)
| Scheme | Marks |
|---|---|
| \(\frac{5}{6} \times \frac{1}{6} \times \frac{1}{6}\) oe | M1 |
| × 3 | M1 |
| \(\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}\) oe | M1 |
| \(\frac{2}{27}\) or \(\frac{16}{216}\) or 0.074… | A1 |
| (4) | |
| (4 marks) |
Notes
M1: or \(15 \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}\): M2
M1: or \(16 \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}\): M3
Dep on 1 − : \((\frac{5}{6})^2 \times \frac{1}{6}\) × 3, \((\frac{5}{6})^3\)