| Date | November 2015 | Marks available | 2 | Reference code | 15N.2.hl.TZ0.1 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Hence and Show that | Question number | 1 | Adapted from | N/A |
Question
The events \(A\) and \(B\) are such that \({\text{P}}(A) = 0.65\), \({\text{P}}(B) = 0.48\) and \({\text{P}}(A \cup B) = 0.818\).
Find \({\text{P}}(A \cap B)\).
[2]
a.
Hence show that the events \(A\) and \(B\) are independent.
[2]
b.
Markscheme
Note: In Section A, where appropriate, accept answers that correctly round to 2 sf except in Q2, Q5(a) (ii), Q5(b) and Q8(a).
\(0.818 = 0.65 + 0.48 - {\text{P}}(A \cap B)\) (M1)
\({\text{P}}(A \cap B) = 0.312\) A1
[2 marks]
a.
\({\text{P}}(A)P(B) = 0.312\;\;\;( = 0.48 \times 0.65)\) A1
since \({\text{P}}(A)P(B) = {\text{P}}(A \cap B)\) then \(A\) and \(B\) are independent R1
Note: Only award the R1 if numerical values are seen. Award A1R1 for a correct conditional probability approach.
[2 marks]
Total [4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
