O-LevelMathematicsProbability4024/21 · Oct/Nov 2018 · Q48 Marks
(a) = {x: x is an integer 1 ≤ x ≤ 10} A = {x : x is a factor of 20} B = {x: x is a multiple of 4}
- (a)(i)Complete the Venn diagram. [Figure 4.1][2]
- (a)(ii)State n(AUB).[1]
- (a)(iii)Describe in words the set A∩B'.[1]
- (b)30 people are asked what type of fruit they like. Of these people, • 5 say they like both oranges and bananas • 12 say they like oranges • 8 say they like neither oranges nor bananas.
- (b)(i)By drawing a Venn diagram, or otherwise, find the number of people who like bananas but not oranges.[2]
- (b)(ii)Two of the 30 people are selected at random. Find the probability that they both like oranges but not bananas.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [2] B1 for 8 or 9 numbers correctly placed
- or for 1, 2, 4, 5, 8, 10 correctly placed with no numbers placed incorrectly
- [1] 6
- FT n(AB) from their Venn diagram
- [1] Factors of 10 oe
- [2] 10
- B1 for Venn diagram with at least 3 numbers correct
- Or M1 for 30 = 8 + 12 + x oe
- [2] 42/870 or 7/145 oe
- M1 for their 7/30 × their 6/29 [x2]
- or SC1 for answer 49/900 oe, FT their Venn diagram
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