Higher November 2017 Paper 3 Q14
14 In the Venn diagram
ξ represents 31 students in a class
\(C\) is students who have a cat
\(D\) is students who have a dog
(a) One student from the class is picked at random.
Work out the probability that the student has a dog. [3 marks]
(b) One of the students who has a cat is picked at random.
Work out the probability that this student has a dog. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(6 + 5 + 2x + x + 2 = 31\) or \(3x + 13 = 31\) or \(3x = 18\) or \(\dfrac{5 + 2x}{31}\) or \(\dfrac{5 + 2x}{3x + 13}\) | M1 | oe equation \(6 + 5 + 2(6) + 6 + 2 = 31\) (embedded answer) |
| (\(x =\)) 6 | A1 | |
| \(\dfrac{17}{31}\) or 0.548… or 0.55 or 54.8…% or 55% | A1ft | ft \(\dfrac{5 + \text{their } 2x}{31}\) and M1 A0 or ft \(\dfrac{23 - \text{their } x}{31}\) and M1 A0 |
Additional guidance
| \(x = 6\), answer \(\dfrac{12}{31}\) or answer \(\dfrac{12}{31}\) alone (implied \(x = 6\)) | M1A1A0 |
| \(3x = 18\), \(x = 5\), answer \(\dfrac{15}{31}\) or \(\dfrac{18}{31}\) | M1A0A1ft |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{5}{11}\) or 0.45… or 45.(…)% | B1 | oe |