4400 Higher June 2007 Paper 4 Q18
18 A fair, 6-sided dice has faces numbered 1, 2, 3, 4, 5 and 6
When the dice is thrown, the number facing up is the score.
The dice is thrown three times.
(a) Calculate the probability that the total score is 18 (2)
(b) Calculate the probability that the score on the third throw is exactly double the total of the scores on the first two throws. (4)
| Scheme | Marks |
|---|---|
| \(\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6}\) alone | M1 |
| \(\frac{1}{216}\) or 0.0046... | A1 |
| (2) |
Notes
M1: \(0.17^3\) or \(0.16^3\) or better. Not \(\times k\)
| Scheme | Marks |
|---|---|
| 1,1,4 or 1,2,6 or 2,1,6 seen or implied | M1 |
| 1, 1, 4 and 1, 2, 6 (or 2, 1, 6) seen or implied | M1 |
| \((\frac{1}{6})^3 \times 3\) | M1 |
| \(\frac{1}{72}\) or \(\frac{3}{216}\) or 0.014 or better | A1 |
| (4) | |
| (6 marks) |
Notes
M1: ie one route
M1: ie two routes incl 1, 1, 4
M1: ie three routes and correct exp’n
A1: \((\frac{1}{6})^3 \times 2\) or \(\frac{1}{108}\), no wking: M0A0