4MA0 Higher January 2016 Paper 3R Q4
4 Maisie plays a game.
Each time she plays, she can win a prize of $1 or $5 or $10
When she does not win one of these prizes, she loses.
The table gives the probability of winning each of the prizes.
| Prize | Probability |
|---|---|
| $1 | 0.50 |
| $5 | 0.15 |
| $10 | 0.05 |
Maisie plays the game once.
(a) Work out the probability that Maisie loses. (2)
(b) Maisie plays the game 40 times.
(i) Work out an estimate for the number of $5 prizes she wins. (2)
(ii) Work out an estimate for the total value of the prizes she wins. (3)
| Scheme | Marks |
|---|---|
| \(1 - 0.5 - 0.15 - 0.05\) | M1 |
| 0.3 | A1 |
| (2) |
(i)
| Scheme | Marks |
|---|---|
| \(40 \times 0.15\) | M1 |
| 6 | A1 |
| (2) |
Notes
M1: Accept 40 × 0.15 × 5 or 6 × 5 or 30
(ii)
| Scheme | Marks |
|---|---|
| \(40 \times 0.5\) or 20 and \(40 \times 0.05\) or 2 | M1 |
| "20" × 1 + "6" × 5 + "2" × 10 | M1 |
| 70 | A1 |
| (3) |
Notes
M1: Dep
ft from (i)
Alternative method
| Scheme | Marks |
|---|---|
| 1 × 0.50 + 5 × 0.15 + 10 × 0.05 or 1.75 | M1 |
| “1.75” × 40 | M1 |
| 70 | A1 |
Notes
M1: Dep