| Date | May 2015 | Marks available | 2 | Reference code | 15M.1.hl.TZ2.1 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
\(A\) and \(B\) are two events such that \({\text{P}}(A) = 0.25,{\text{ P}}(B) = 0.6\) and \({\text{P}}(A \cup B) = 0.7\).
Find \({\text{P}}(A \cap B)\).
Determine whether events \(A\) and \(B\) are independent.
Markscheme
\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\)
\({\text{P}}(A \cap B) = 0.25 + 0.6 = 0.7\) M1
\( = 0.15\) A1
[2 marks]
EITHER
\({\text{P}}(A){\text{P}}(B)( = 0.25 \times 0.6) = 0.15\) A1
\( = {\text{P}}(A \cap B)\) so independent R1
OR
\({\text{P}}(A|B) = \frac{{{\text{P}}(A \cap B)}}{{{\text{P}}(B)}} = \frac{{0.15}}{{0.6}} = 0.25\) A1
\( = {\text{P}}(A)\) so independent R1
Note: Allow follow through for incorrect answer to (a) that will result in events being dependent in (b).
[2 marks]
Total [4 marks]
