| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.sl.TZ1.1 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
In a group of 20 girls, 13 take history and 8 take economics. Three girls take both history and economics, as shown in the following Venn diagram. The values pp and qq represent numbers of girls.
Find the value of pp;
[2]
a.i.
Find the value of qq.
[2]
a.ii.
A girl is selected at random. Find the probability that she takes economics but not history.
[2]
b.
Markscheme
valid approach (M1)
egp+3=13, 13−3p+3=13, 13−3
p=10p=10 A1 N2
[2 marks]
a.i.
valid approach (M1)
egp+3+5+q=20, 10−10−8p+3+5+q=20, 10−10−8
q=2q=2 A1 N2
[2 marks]
a.ii.
valid approach (M1)
eg20−p−q−3, 1−1520, n(E∩H′)=5
520(14) A1 N2
[2 marks]
b.
Examiners report
[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.
