Higher June 2018 Paper 1 Q15
15 A biased dice is thrown.
Here are the probabilities of each score.
| Score | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Probability | 0.25 | 0.05 | 0.15 | 0.05 | 0.3 | 0.2 |
The dice is thrown 200 times.
Work out the expected number of times the score will be odd. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(0.25 + 0.15 + 0.3\) or 0.7 | M1 | oe eg \(1 - 0.05 - 0.05 - 0.2\) |
| their \(0.7 \times 200\) | M1dep | oe implied by \(\dfrac{140}{200}\) |
| 140 | A1 | |
| Alternative method 2 | ||
| \(0.25 \times 200\) or 50 or \(0.15 \times 200\) or 30 or \(0.3 \times 200\) or 60 | M1 | oe |
| \(0.25 \times 200 + 0.15 \times 200 + 0.3 \times 200\) or \(50 + 30 + 60\) | M1dep | oe implied by \(\dfrac{140}{200}\) |
| 140 | A1 | |
| Alternative method 3 | ||
| \((0.05 + 0.05 + 0.2) \times 200\) or \(2 \times 0.05 \times 200 + 0.2 \times 200\) or \(2 \times 10 + 40\) or 60 | M1 | oe |
| \(200 -\) their 60 | M1dep | oe implied by \(\dfrac{140}{200}\) |
| 140 | A1 | |
Additional guidance
| Ignore attempt to simplify \(\dfrac{140}{200}\) | M1M1A0 |
| \(\dfrac{140}{200}\) and 140 both on answer line | M1M1A0 |
| Do not allow a misread of any probability |