Higher June 2023 Paper 2R Q19
19 30 adults booked to stay in a hotel.
19 adults booked breakfast
15 adults booked dinner
4 adults did not book breakfast or dinner
Some adults booked breakfast and dinner.
Meihui chooses at random two of the 30 adults.
Work out the probability that these two adults each booked breakfast and dinner.
(4)
| Scheme | Marks |
|---|---|
| (19 + 15 + 4) – 30 or 38 – 30 or 19 + 15 – 26 or  \(19 - x + x + 15 - x + 4 = 30\) oe | M1 |
| 8 | A1 |
\(\dfrac{8}{30} \times \dfrac{7}{29}\) or \(\dfrac{8}{30} \times \dfrac{8}{30} = \dfrac{64}{900}\) or \(\dfrac{16}{225}\) oe | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{28}{435}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct method to find the number of people booking breakfast and dinner
A1: can be shown in a Venn diagram or a valid calculation
M1: for the use of \(\dfrac{k}{30} \times \dfrac{k - 1}{29}\) where \(k \lt 30\)
or \(\dfrac{\text{``}8\text{''}}{n} \times \dfrac{\text{``}8\text{''} - 1}{n - 1}\) where \(n \gt 8\)
A1: oe awrt 0.064 or awrt to 6.4%
M1A1 for a fully correct Venn diagram
or for \(\dfrac{8}{30}\)