Find ${\rm{P}}(A)$ .

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

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

${\rm{P}}(A) = \frac{1}{{11}}$     A1    N1

[1 mark]

${\rm{P}}(B|A) = \frac{2}{{10}}$     A2     N2

[2 marks]

recognising that ${\rm{P}}(A \cap B) = {\rm{P}}(A) \times {\rm{P}}(B|A)$     (M1) 

correct values     (A1)

e.g. ${\rm{P}}(A \cap B) = \frac{1}{{11}} \times \frac{2}{{10}}$

${\rm{P}}(A \cap B) = \frac{2}{{110}}$     A1     N3 

[3 marks]

Most candidates answered part (a) correctly.

Few candidates used the concept of "B given A" to simply "write down" the answer of $\frac{2}{{10}}$ . Instead, most reached for the formula in the booklet, with which few were successful.

Few also made the connection that part (c) could be answered using both previous answers. Many found ${\rm{P}}(A \cap B)$ correctly even when answering part (b) incorrectly, although some candidates did not decrease the denominator for the second event.