Find ${\text{P}}(A \cap B)$.

Hence show that the events $A$ and $B$ are independent.

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]

${\text{P}}(A)P(B) = 0.312\;\;\;( = 0.48 \times 0.65)$     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]