Given that $A$ and $B$ are mutually exclusive, find ${\text{P}}(B)$.

Given that $A$ and $B$ are independent, find ${\text{P}}(B)$.

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]