Find the value of ${\text{P}}(A \cup B)$ when
(i)     $A$ and $B$ are mutually exclusive;
(ii)     $A$ and $B$ are independent.

Given that ${\text{P}}(A \cup B) = 0.6$ , find ${\text{P}}(A|B)$ .

(i)     ${\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) = 0.7$     A1

(ii)     ${\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)$     (M1)

  $= {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A){\text{P}}(B)$     (M1)

  $= 0.3 + 0.4 - 0.12 = 0.58$     A1

[4 marks]

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

$= 0.3 + 0.4 - 0.6 = 0.1$     A1

${\text{P}}(A|B) = \frac{{{\text{P}}(A \cap B)}}{{{\text{P}}(B)}}$     (M1)

$= \frac{{0.1}}{{0.4}} = 0.25$     A1

[3 marks]

Most candidates attempted this question and answered it well. A few misconceptions were identified (eg ${\text{P}}(A \cup B) = {\text{P}}(A){\text{P}}(B)$ ). Many candidates were unsure about the meaning of independent events.

Most candidates attempted this question and answered it well. A few misconceptions were identified (eg ${\text{P}}(A \cup B) = {\text{P}}(A){\text{P}}(B)$ ). Many candidates were unsure about the meaning of independent events.