Higher June 2024 Paper 6 Q3
3 The word MATHEMATICS is spelt using tiles.
| M | A | T | H | E | M | A | T | I | C | S |
The tiles are put into an empty bag.
One at a time, 99 children each take a tile at random from the bag.
They record the letter and then put the tile back in the bag.
Work out how many times the letter M is expected to be taken from the bag. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 18 nfww | 3 | B2 for answer \(\frac{18}{99}\) | |
| or M2 for \(\frac{2 \times 99}{11}\) oe | e.g. \(\frac{99}{11} = 9\) and then 2 × 9 | ||
| or B1 for \(\frac{2}{11}\) | For B1 accept \(\frac{2}{11}\), 0.181 to 0.182 or 18.1% to 18.2% | ||
| or M1 for [\(k \times\)] \(\frac{99}{11}\) | Condone \(k\) as 0.5 or 1 or an integer \(3 \leqslant k \leqslant 10\) Do not imply M1 from just 9 seen | ||
| or M1 for \(\frac{a}{b} \times 99\) | \(0 \lt \frac{a}{b} \lt 1\) and either \(a = 2\) or \(b = 11\) | ||