| Date | May 2016 | Marks available | 3 | Reference code | 16M.1.sl.TZ1.2 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The following Venn diagram shows the events \(A\) and \(B\), where \({\text{P}}(A) = 0.4,{\text{ P}}(A \cup B) = 0.8\) and \({\text{P}}(A \cap B) = 0.1\). The values \(p\) and \(q\) are probabilities.
(i) Write down the value of \(q\).
(ii) Find the value of \(p\).
Find \({\text{P}}(B)\).
Markscheme
(i) \(q = 0.1\) A1 N1
(ii) appropriate approach (M1)
eg\(\,\,\,\,\,\)\({\text{P}}(A) - q,{\text{ }}0.4 - 0.1\)
\(p = 0.3\) A1 N2
[3 marks]
valid approach (M1)
eg \(\,\,\,\,\,\)\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B),{\text{ P}}(A \cap B) + {\text{P}}(B \cap A')\)
correct values (A1)
eg\(\,\,\,\,\,\)\(0.8 = 0.4 + {\text{P}}(B) - 0.1,{\text{ }}0.1 + 0.4\)
\({\text{P}}(B) = 0.5\) A1 N2
[3 marks]
Examiners report
This question was well done by most candidates. In part (b), the intersection \({\text{P}}(A \cap B)\) was sometimes overlooked, incorrectly using \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B)\) instead.
This question was well done by most candidates. In part (b), the intersection \({\text{P}}(A \cap B)\) was sometimes overlooked, incorrectly using \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B)\) instead.
