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

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

Decide whether A and B are independent events. Give a reason for your answer.

$0.8 = 0.5 + 0.6 - {\text{P}}(A \cap B)$     (M1)
${\text{P}}(A \cap B) = 0.3$     (A1)     (C2)

Note: Award (M1) for correct substitution, (A1) for correct answer.

[2 marks]

${\text{P}}(A|B) = \frac{{0.3}}{{0.6}}$     (M1)

= 0.5     (A1)(ft)     (C2)

Note: Award (M1) for correct substitution in conditional probability formula. Follow through from their answer to part (a), provided probability is not greater than one.

[2 marks]

${\text{P}}(A \cap B) = {\text{P}}(A) \times {\text{P}}(B)$ or 0.3 = 0.5 × 0.6     (R1)

OR

${\text{P}}(A|B) = {\text{P}}(A)$     (R1)

they are independent. (Yes)     (A1)(ft)     (C2)

Note: Follow through from their answers to parts (a) or (b).

Do not award (R0)(A1).

[2 marks]

Parts (a) and (b) were well answered but very few candidates could provide a reason for the independence of A and B. A number of candidates confused independent and mutually exclusive events.

Parts (a) and (b) were well answered but very few candidates could provide a reason for the independence of A and B. A number of candidates confused independent and mutually exclusive events.

Parts (a) and (b) were well answered but very few candidates could provide a reason for the independence of A and B. A number of candidates confused independent and mutually exclusive events.