16N.1.SL.TZ0.S_5

pestleMathematicsAISLPaper 116N· sl-4-5-probability-concepts-expected-numberssource ↗

Events $A$ and $B$ are independent with ${\text{P}}(A \cap B) = 0.2$ and ${\text{P}}(A' \cap B) = 0.6$ .

Find ${\text{P}}(B)$ .

[2]

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

[4]

Markscheme / solution

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

valid interpretation (may be seen on a Venn diagram) (M1)

eg $\,\,\,\,\,$ ${\text{P}}(A \cap B) + {\text{P}}(A' \cap B),{\text{ }}0.2 + 0.6$

${\text{P}}(B) = 0.8$ A1 N2

[2 marks]

valid attempt to find ${\text{P}}(A)$ (M1)

eg $\,\,\,\,\,$ ${\text{P}}(A \cap B) = {\text{P}}(A) \times {\text{P}}(B),{\text{ }}0.8 \times A = 0.2$

correct working for ${\text{P}}(A)$ (A1)

eg $\,\,\,\,\,$ $0.25,{\text{ }}\frac{{0.2}}{{0.8}}$

correct working for ${\text{P}}(A \cup B)$ (A1)

eg $\,\,\,\,\,$ $0.25 + 0.8 - 0.2,{\text{ }}0.6 + 0.2 + 0.05$

${\text{P}}(A \cup B) = 0.85$ A1 N3

[4 marks]

Examiners’ report

[N/A]