Foundation June 2024 Paper 1R Q17
17 Here is a biased spinner.
The table gives information about the probability that, when the spinner is spun once, it will land on each number.
| Number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Probability | \(2x\) | 0.27 | 0.04 | \(x\) | 0.12 |
Alexis is going to spin the spinner 400 times.
Work out an estimate for the number of times the spinner will land on an odd number.
(4)
| Scheme | Marks |
|---|---|
| 1 – (0.27 + 0.04 + 0.12) (= 0.57) oe or \(2x + 0.27 + 0.04 + x + 0.12 = 1\) oe or 0.27 × 400 (= 108) and 0.04 × 400 (= 16) and 0.12 × 400 (= 48) | M1 |
(\(x\) =) “0.57” ÷ 3 (= 0.19) or (\(2x\) =) “0.57” ÷ 3 × 2 (= 0.38) or \(\dfrac{400 - \text{``}{108}\text{''} - \text{``}{16}\text{''} - \text{``}{48}\text{''}}{3}\ (= 76)\) oe or \(\dfrac{400 - \text{``}{108}\text{''} - \text{``}{16}\text{''} - \text{``}{48}\text{''}}{3} \times 2\ (= 152)\) oe | M1 |
| (2 × “0.19” + 0.04 + 0.12) × 400 or 2 × “76” + “16” + “48” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 216 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for showing a clear understanding that the total of probabilities is 1 or for finding estimates for the number of times the spinner will land on 2 and 3 and 5
M1: for a method to find the value of \(x\) or \(2x\) or an estimate for the number of times the spinner will land on 4 or 1
M1: for a complete method
A1: for an answer of 216
answer of \(\dfrac{216}{400}\) oe scores M3A0