Higher June 2022 Paper 6 Q12
12 A student has a spinner with sectors numbered 1, 2, 3 and 4.
The table shows the probability of each score.
| Score | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Probability | 0.4 | 0.3 | 0.2 | 0.1 |
The student spins the spinner twice.
Calculate the probability that the student gets the same score on each spin. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 0.3 oe nfww | 4 | M3 for \(0.4^2 + 0.3^2 + 0.2^2 + 0.1^2\) oe or M2 for \(0.4^2\) oe and \(0.3^2\) oe and \(0.2^2\) oe and \(0.1^2\) oe or M1 for \(0.4^2\) oe or \(0.3^2\) oe or \(0.2^2\) oe or \(0.1^2\) oe | M2 for correct method spoilt e.g. \(\dfrac{0.4^2 + 0.3^2 + 0.2^2 + 0.1^2}{4}\) Likely equivalents: \(0.4^2\) = 0.16 or \(\frac{4}{25}\) or 16% \(0.3^2\) = 0.09 or \(\frac{9}{100}\) or 9% \(0.2^2\) = 0.04 or \(\frac{1}{25}\) or 4% \(0.1^2\) = 0.01 or \(\frac{1}{100}\) or 1% |