Foundation June 2019 Paper 2 Q14
14 There are 135 passengers on a plane.
3 of the passengers in Business Class are flying for the first time.
In total, there are 15 passengers in Business Class.
\(\dfrac{1}{4}\) of the passengers not in Business Class are flying for the first time.
(a) In the Venn diagram,
\(\xi\) = passengers on the plane
B = passengers in Business Class
F = passengers flying for the first time.
Complete the Venn diagram. [4 marks]
(b) One of the passengers is chosen at random.
Write down the probability that the passenger is in Business Class. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| 3 in the intersection | B1 | |
| 12 in the left hand part of B | B1 | |
| 30 in the right hand part of F | B1 | |
| All four sections total 135 | B1 | must be using integers > 0 and have one integer in each of the four sections |
Additional guidance
| Mark the diagram | |
| Ignore any correct or incorrect numbers on the diagram outside the rectangle eg 135 | |
 | B1B1B1B1 |
 | B1B0B1B1 |
 | B1B0B1B0 |
 | B1B0B0B1 |
| Two integers in one section is choice and doesn’t score the mark for that section or the final mark | |
| Condone multiple letters or tallies or crosses etc instead of numbers for all the marks |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{15}{135}\) or \(\dfrac{5}{45}\) or \(\dfrac{3}{27}\) or \(\dfrac{1}{9}\) or \(0.\dot{1}\) or 0.11(1…) or 11(.1…)% | B1 | oe fraction decimal or percentage |
Additional guidance
| Ignore attempts to simplify or convert a correct fraction to a decimal or percentage | |
| 15 out of 135 | B0 |
| 0.1 without correct fraction seen | B0 |
| Ratio | B0 |