O-LevelMathematicsProbability4024/22 · Oct/Nov 2017 · Q67 Marks
(a) & = {x : x is an integer and 10 ≤ x ≤ 20} A = {x : x is an odd number} B = {x : x is a multiple of 5} (b) In a survey, 40 people were asked what they had read that day. • A total of 10 people had read a book • A total of 24 people had read a newspaper • 14 people had read neither a book nor a newspaper
- (a)(i)Find n(A ∩ B).[1]
- (a)(ii)Find A' U B.[1]
- (a)(iii)A number, r, is chosen at random from &. Find the probability that r ∈ A U B.[1]
- (b)(i)By drawing a Venn diagram, or otherwise, find the number of people who had read both a book and a newspaper.[2]
- (b)(ii)Two of the 10 people who had read a book are selected at random. Work out the probability that they had both read a book and a newspaper.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] (a)(i) 1
- [1] (a)(ii) 10, 12, 14, 15, 16, 18, 20
- [1] (a)(iii) 7/11 oe
- [2] (b)(i) 8
- M1 for 14 +10+24-x = 40 oe
- or for correct Venn diagram with algebraic expressions.
- Or B1 for Venn diagram with at least 3 numbers correct
- [2FT] (b)(ii) 28/45 oe
- M1 for (their 8)/(10) × (their 7)/(9) [x2] where k > their 8
- Or SC1 for (their 8)² / (10)
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