Higher November 2021 Paper 5 Q16

OCRHigherCurrent spec5 marksBasic Probability Sets

16 In a group of 60 students, 40 own a smartphone, 27 own a tablet and 8 own neither.

A student is chosen at random from those that own a tablet.

Find the probability that they also own a smartphone.
You must show your working. [5]

Mark scheme

Answer	Marks
\(\dfrac{15}{27}\) oe with correct working	5	isw cancelling/conversion to other forms
With \(x\) representing the number of smartphone and tablet: B3 for [smartphone and tablet =] 15 may be on a Venn diagram oe or M2 for [\(x\) = ] 40 + 27 + 8 – 60 oe or M1 for \(40 - x + x + 27 - x + 8 = 60\) oe or for Venn diagram with \(40 - x\), \(x\) and \(27 - x\) correctly placed	For full marks “correct working” requires B3 ie [smartphone and tablet =] 15 with evidence of M1 or M2 or alternate convincing approach M1 FT their 15 provided < 27 For Venn diagrams, condone omission of universal set rectangle and 8 for M1, M2, B3 and full marks
and M1 for fraction \(\dfrac{n}{27}\) or \(\dfrac{15}{n}\) that leads to the answer If 0 scored SC2 for \(\dfrac{15}{27}\) oe with no working	For M1 must be a proper fraction

Answer

Marks

Part marks and guidance

\(\dfrac{15}{27}\) oe
with correct working

isw cancelling/conversion to other forms

With \(x\) representing the number of smartphone and tablet:

B3 for [smartphone and tablet =] 15 may be on a Venn diagram oe
or M2 for [\(x\) = ] 40 + 27 + 8 – 60 oe
or M1 for \(40 - x + x + 27 - x + 8 = 60\) oe
or for Venn diagram with \(40 - x\), \(x\) and \(27 - x\) correctly placed

For full marks “correct working” requires B3 ie [smartphone and tablet =] 15 with evidence of M1 or M2 or alternate convincing approach

M1 FT their 15 provided < 27
For Venn diagrams, condone omission of universal set rectangle and 8 for M1, M2, B3 and full marks

and
M1 for fraction \(\dfrac{n}{27}\) or \(\dfrac{15}{n}\) that leads to the answer

If 0 scored
SC2 for \(\dfrac{15}{27}\) oe with no working

For M1 must be a proper fraction