| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.sl.TZ0.5 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 5 | Adapted from | N/A |
Question
Events \(A\) and \(B\) are independent with \({\text{P}}(A \cap B) = 0.2\) and \({\text{P}}(A' \cap B) = 0.6\).
Find \({\text{P}}(B)\).
Find \({\text{P}}(A \cup B)\).
Markscheme
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]
