Foundation November 2024 Paper 2 Q21
21 Cody has a biased 5-sided spinner, numbered 1, 2, 3, 4, 5
The table gives the probabilities that when the spinner is spun it will land on 2 or on 3 or on 5
| Number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Probability | 0.14 | 0.17 | 0.21 |
The probability that the spinner will land on 1 is the same as the probability that the spinner will land on 4
Cody is going to spin the spinner 400 times.
Work out an estimate for the number of times the spinner will land on 4
(4)
| Scheme | Marks |
|---|---|
| 1 – (0.14 + 0.17 + 0.21) (= 0.48) or \(0.14 + 0.17 + 0.21 + 2x = 1\) oe or 0.14 × 400 (= 56) or 0.17 × 400 (= 68) or 0.21 × 400 (= 84) or (0.14 + 0.17 + 0.21) × 400 (= 208) oe eg 0.52 × 400 (= 208) | M1 |
| “0.48” ÷ 2 (= 0.24) [could be seen in table] or 400 – 56 – 68 – 84 (= 192) oe eg 400 – 208 (= 192) or 0.48 × 400 (= 192) | M1 |
| “0.24” × 400 oe or 192 ÷ 2 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 96 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Correct use of probabilities total 1
or
correct calculation for an estimate for number of times the spinner will land on 2 or on 3 or on 5
M1: A completely correct method to find the probability that the spinner will land on 4
or
a completely correct method to find the number of times the spinner will land on 1 or on 4
A1: cao
SCB1 for 104 if no other marks have been awarded