O-LevelMathematicsProbability4024/22 · Oct/Nov 2019 · Q58 Marks

= {x: x is an integer 1 ≤ x ≤ 16} A = {x : x is an even number} B = {x: x is a square number} C = {x: x is a factor of 100}

(a)(i)Complete the Venn diagram.[3]
(a)(ii)Find n(A'∪B).[1]
(a)(iii)p ∈ A ∩ C Write down all the possible values of p.[1]
(b)(i)Ateeq has a set of 16 cards numbered from 1 to 16. He takes a card from the set at random. Find the probability that the card shows an odd square number.[1]
(b)(ii)Ateeq takes two cards at random from the set of 16 cards. Find the probability that both cards show even numbers that are factors of 100.[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 2019). The mark or mark type is shown in brackets.

[3] Correctly completed Venn diagram
[3] 6, 8, 12 in A∩C'
[3] 14 in A∩B'
[3] 16 in A∩B∩C
[3] 9 in B∩A'C'
[3] 2, 10, 4 in C∩A'B'
[3] 1 in B∩C'
[3] 5 in B'C'A'
[3] 3, 7, 11, 13, 15 in universal set (outside circles)
[3] B2 for Venn diagram with one or two errors, omissions or repeats or for correct Venn diagram with 3, 7, 11, 13, 15 omitted
[3] or B1 for Venn diagram with three or four errors, omissions or repeats or for correct Venn diagram with 3, 7, 11, 13, 15 omitted and one other error, omission or repeat
[1] 10
[1] 2, 4, 10
[1] FT their Venn diagram
[1] 1/8 oe
[2] 1/40 oe
[2] M1 for (k/16) × ((k-1)/15) where k is 4, 3, or 2 or 4/16 × 3/15 oe

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.