Multiple Events: Eduqas GCSE Higher June 2019 Paper 2 Q19

Higher June 2019 Paper 2 Q19

EduqasHigherCurrent spec6 marksMultiple Events

19. The driving theory test consists of 50 questions.
At least 43 of these questions must be answered correctly to pass the test.
For each question in the test, four possible answers are given. Only one of these answers is correct.

Waldo takes the test.
Waldo knows 78% of the facts assessed in the test.
For each question based on these facts he selects the correct answer.

On all other questions he randomly selects one of the four possible answers.

(a) A question is selected at random from the paper.
Calculate the probability that Waldo correctly answers the question. [4]

(b) Is Waldo likely to pass his driving theory test?

Yes ☐ No ☐

You must show all your working to support your answer. [2]

Mark scheme (a)

Scheme	Marks	Comments
\(0.78 \times 1\) or equivalent, AND an attempt to consider the other 22%	M1	Not for sight of 78% alone
\(0.22 \times \frac14\) or equivalent	M1
Showing the need to add \((0.78 + 0.055)\)	M1	Method considers 78% + 22% of \(\frac14\)
0.835 or 83.5%	A1

Alternative

Scheme	Marks	Comments
(Number of questions) \(0.78 \times 50 + (50 - 0.78 \times 50) \times 0.25\)	M1
\((= 39 + 2.75 =)\ 41.75\)	A1
(Probability) \(41.75/50\)	M1	(FT from M1)
\(= 0.835\)	A1

Mark scheme (b)

Scheme	Marks	Comments
Probability from part (a) \(\times 50\)	M1	FT from part (a), apart from 78% giving an answer of 39, this is M0 A0
41.75 with interpretation ‘No’	A1	FT from part (a), apart from 78%, with appropriate interpretation \(\geqslant 43\) as ‘yes’ or \(\lt 43\) as ‘no’ Award M1 A1 for an appropriate conclusion without working only if the alternative method is used in (a)
	(6)

Alternative 1

Scheme	Marks	Comments
(43/50 as) 86% compared with probability 83.5%	M1
Interpretation ‘No’	A1

Alternative 2

Scheme	Marks	Comments
(With 83.5% seen in (a)) 41 or 42 questions correct	M1
Interpretation ‘No’	A1