Foundation January 2023 Paper 1 Q22
22 Some members of a library were asked to name the type of book that they each liked to read the best.
One of the members is chosen at random.
The table shows information about the probability of the type of book that this member answered.
| Type of book | comedy | romance | mystery | thriller |
|---|---|---|---|---|
| Probability | 0.24 | 0.40 | \(3x\) | \(x\) |
48 members answered comedy books.
Work out how many of the members answered mystery books.
(4)
| Scheme | Marks |
|---|---|
| 1 – (0.24 + 0.4) (= 0.36) oe or \(3x + x\) = 1 – (0.24 + 0.4) oe | M1 |
| 48 ÷ 0.24 (= 200) or “0.36” ÷ 4 (= 0.09) or “0.36” ÷ 4 × 3 (= 0.27) | M1 |
| “0.27” × “200” or “200” × “0.36” ÷ 4 × 3 (“200” – 48 – “80”) ÷ 4 × 3 | M1 |
| 54 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a complete method
| Scheme | Marks |
|---|---|
| 1 – (0.24 + 0.4) (= 0.36) oe or \(3x + x\) = 1 – (0.24 + 0.4) oe | M1 |
48 ÷ 24 (= 2) oe or \(\left(\dfrac{\text{“}0.36\text{”}}{4} \times 3\right) \div 0.24\;\left(= \dfrac{9}{8} = 1.125\right)\) oe or \(\left(\dfrac{\text{“}36\text{”}}{4} \times 3\right) \div 24\;\left(= \dfrac{9}{8} = 1.125\right)\) oe | M1 |
\(\text{“}2\text{”} \times \left(\dfrac{\text{“}36\text{”}}{4} \times 3\right)\) oe or \(\text{“}\tfrac{9}{8}\text{”} \times 48\) oe or \((\text{“}27\text{”} \div 24) \times 48\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 54 | A1 |
Notes
M1: for a complete method