17M.2.AHL.TZ1.H_1

pestleMathematicsAAHLPaper 217M· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

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]

Find ${\text{P}}(A' \cap B)$ .

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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]

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]

Examiners’ report

[N/A]