| Date | November 2013 | Marks available | 4 | Reference code | 13N.2.sl.TZ0.4 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Two events \(A\) and \(B\) are such that \({\text{P}}(A) = 0.2\) and \({\text{P}}(A \cup B) = 0.5\).
Given that \(A\) and \(B\) are mutually exclusive, find \({\text{P}}(B)\).
Given that \(A\) and \(B\) are independent, find \({\text{P}}(B)\).
Markscheme
correct approach (A1)
eg \(0.5 = 0.2 + {\text{P}}(B),{\text{ P}}(A \cap B) = 0\)
\({\text{P}}(B) = 0.3\) A1 N2
[2 marks]
Correct expression for \({\text{P}}(A \cap B)\) (seen anywhere) A1
eg \({\text{P}}(A \cap B) = 0.2{\text{P}}(B),{\text{ }}0.2x\)
attempt to substitute into correct formula for \({\text{P}}(A \cup B)\) (M1)
eg \({\text{P}}(A \cup B) = 0.2 + {\text{P}}(B) - {\text{P}}(A \cap B),{\text{ P}}(A \cup B) = 0.2 + x - 0.2x\)
correct working (A1)
eg \(0.5 = 0.2 + {\text{P}}(B) - 0.2{\text{P}}(B),{\text{ }}0.8x = 0.3\)
\({\text{P}}(B) = \frac{3}{8}{\text{ }}( = 0.375,{\text{ exact}})\) A1 N3
[4 marks]
