| Date | May 2017 | Marks available | 3 | Reference code | 17M.2.hl.TZ1.1 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Calculate | Question number | 1 | Adapted from | N/A |
Question
Consider two events \(A\) and \(B\) such that \({\text{P}}(A) = k,{\text{ P}}(B) = 3k,{\text{ P}}(A \cap B) = {k^2}\) and \({\text{P}}(A \cup B) = 0.5\).
Calculate \(k\);
[3]
a.
Find \({\text{P}}(A' \cap B)\).
[3]
b.
Markscheme
use of \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\) M1
\(0.5 = k + 3k - {k^2}\) A1
\({k^2} - 4k + 0.5 = 0\)
\(k = 0.129\) A1
Note: Do not award the final A1 if two solutions are given.
[3 marks]
a.
use of \({\text{P}}(A' \cap B) = {\text{P}}(B) - {\text{P}}(A \cap B)\) or alternative (M1)
\({\text{P}}(A' \cap B) = 3k - {k^2}\) (A1)
\( = 0.371\) A1
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
