Foundation June 2023 Paper 2 Q14
14.
(a)
Geomet High School has 740 students.
Each student was asked which method of travel listed below was their main method of travel to school.
The table below shows the methods of travel together with some of their probabilities.
| Method of travel | Walk | Bus | Bike | Car | Train | Other |
|---|---|---|---|---|---|---|
| Probability | 0·2 | 0·35 | 0·3 | 0 |
(i)
A student is chosen at random.
What is the probability that this student walks to school or travels to school by bus? [1]
(ii) How many of the 740 students travel to school by bus? [2]
(iii)
The probability that a student travels to school by car is twice the probability that a student travels to school by train.
Calculate the probability that a student travels to school by train. [3]
(b) 
The Venn diagram shows information about the number of students who study Music and Drama in Year 11 at Geomet High School.
There are 104 students in Year 11.
(i) Complete the Venn diagram to show the number of students in Year 11 who do not study Music or Drama. [1]
(ii) What is the probability that a student chosen at random from Year 11 studies Music? [2]
| Scheme | Marks | Comments |
|---|---|---|
| (i) 0.55 oe | B1 | |
| (ii) 0.35 × 740 | M1 | Or equivalent complete and correct method. |
| = 259 | A1 | |
| (iii) 1 – (0.2 + 0.35 + 0.3) oe | M1 | FT 1 – ( ‘their 0.55’ + 0.3 ) |
| ÷ 3 | m1 | |
| = 0.05 oe | A1 | Answer may be seen in the table Answers in the working space take precedence over the table. Note: If answers of 0.1 and 0.05 are offered without labels (or incorrectly labelled) or not given in the table then award M1 m1 A0. |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 62 | B1 | Venn diagram takes precedence |
| (ii) \(\frac{31}{104}\) oe ISW | B2 | B1 for \(\frac{17+14}{104}\) or \(\frac{31}{b}\), where \(b \gt 31\) or \(\frac{17+14}{b}\), where \(b \gt 31\) |
| (9) |