S1 January 2012 Q6

EdexcelOld spec13 marksProbability

6. The following shows the results of a survey on the types of exercise taken by a group of 100 people.

65 run
48 swim
60 cycle
40 run and swim
30 swim and cycle
35 run and cycle
25 do all three

(a) Draw a Venn Diagram to represent these data. (4)

Find the probability that a randomly selected person from the survey

(b) takes none of these types of exercise, (2)

(d) takes at least two of these types of exercise. (2)

Jason is one of the above group.

Given that Jason runs,

(e) find the probability that he swims but does not cycle. (3)

Scheme	Marks

3 closed curves and 25 in correct place	M1
15,10,5	A1
15,3,20	A1
Labels \(R\), \(S\), \(C\) and box	B1
	(4)

Mark scheme (b)

Scheme	Marks
7/100 or 0.07 M1 for (‘their 7’in diagram or here)/100	M1 A1
	(2)

Notes

M1 for ‘their 7’/100 seen.
A1 Correct answer only

In parts (c) and (d) we require “/100” for methods to be awarded. Also check their values and award correct method if they follow from their Venn Diagram.

Scheme	Marks
(3+5)/100 = 2/25 or 0.08	M1A1
	(2)

Scheme	Marks
(25+15+10+5)/100 = 11/20 or 0.55	M1 A1
	(2)

Mark scheme (e)

Scheme	Marks
\(\mathrm{P}(S \cap C' \mid R) = \dfrac{P(S \cap C' \cap R)}{P(R)}\) Require denominator to be ‘their 65’ or ‘their \(\dfrac{65}{100}\)’,	M1
\(= \dfrac{15}{65}\) require ‘their 15’ and correct denominator of 65	A1
\(= \dfrac{3}{13}\) or exact equivalents.	A1
	(3)
	(13 marks)

Notes

M1 Attempt to use correct formula for conditional probability.
Award for correct formula and a denominator of ’their 65’ or ‘their 65/100’.
A1 for ‘their 15’/65 only.
A1 for exact equivalent answers, including 15/65.

In all parts correct answers with no working award full marks.