Higher November 2017 Paper 1 Q15
15. Fifty people order food and drink for a party.
They each order one main course and one drink from the menu.
Menu
| Main course | Drink |
|---|---|
| Pizza | Cola |
| Burger | Water |
| Kebab | Juice |
28 people order cola.
24 people order a burger.
8 people order a kebab and none of these order cola.
The 5 people who order water all order a kebab.
Of the people who order a burger, twice as many order cola as order juice.
A person is selected at random from the group.
Using the table to help you, find the probability that this person orders either a burger and cola or a pizza and juice.
You must show all your working. [7]
| Cola | Water | Juice | ||
|---|---|---|---|---|
| Pizza | ||||
| Burger | ||||
| Kebab | ||||
| Scheme | Marks | Comments | |||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B4 | B1 for the given 24, 28, 8, 0 (shaded) correctly placed B1 for the 5’s and remaining 0’s correctly placed in the water column B1 for 16 and 12 correctly placed or for the 16 and 8 correctly placed B1 for the 18 and 6 correctly placed or for the 17 and 6 correctly placed FT ‘their 16’ & ‘their 12’ or ‘their 16’ & ‘their 8’, i.e. 18 and 18 – ‘their 12’ or 18 and 18 – (28 – ‘their 16’) or 17 and 17 – (8 – ‘their 5’) – ‘their 8’ or 17 and 17 – (8 – ‘their 5’) – (24 – ‘their 16’) May be probabilities or frequencies | |||||||||||||||||||||||||
| \(\dfrac{16 + 6}{50}\) | M2 | FT ‘their 16’ and ‘their 6’ for M1 or M2 M1 for sight of either \(\dfrac{16}{50}\) or \(\dfrac{6}{50}\) or equivalent or sight of ‘their (16 + 6)’ | |||||||||||||||||||||||||
| \(\dfrac{22}{50}\) or equivalent | A1 | CAO | |||||||||||||||||||||||||
| (7) |