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

Determine whether events $A$ and $B$ are independent.

${\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)$

${\text{P}}(A \cap B) = 0.25 + 0.6 = 0.7$     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]