Higher November 2021 Paper 3 Q15
15 A biased spinner can land on A, B or C.
The table shows the probabilities, in terms of \(k\), of A, B and C.
| A | B | C | |
|---|---|---|---|
| Probability | \(0.5k\) | \(7k - 0.15\) | \(2.5k\) |
Work out the probability of B. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.5k + 7k - 0.15 + 2.5k = 1\) | M1 | oe eg \(10k - 0.15 = 1\) |
| \(k = 0.115\) | A1 | oe |
| 0.655 | A1ft | oe eg \(\dfrac{131}{200}\) or 65.5% ft their 0.115 to 3 dp or better with M1 scored if their 0.115 and their answer are both in the range (0, 1) |
Additional guidance
| Accept working in percentages | |
| \(10k - 0.15 = 1,\ 10k = 0.85,\ k = 0.085\), answer 0.445 | M1A0A1ft |
| \(10k + 0.15 = 1,\ 10k = 0.85,\ k = 0.085\), answer 0.445 | M0A0A0 |