Find the probability that they watch a French movie.

Given that last week they watched a French movie, find the probability that it was on a Saturday night.

${\text{P}}(F) = \left( {\frac{1}{7} \times \frac{7}{9}} \right) + \left( {\frac{6}{7} \times \frac{4}{9}} \right)$     (M1)(A1)

Note:     Award M1 for the sum of two products.

$= \frac{{31}}{{63}}{\text{ }}( = 0.4920 \ldots )$     A1

[3 marks]

Use of ${\text{P}}(S|F) = \frac{{{\text{P}}(S \cap F)}}{{{\text{P}}(F)}}$ to obtain ${\text{P}}(S|F) = \frac{{\frac{1}{7} \times \frac{7}{9}}}{{\frac{{31}}{{63}}}}$.     M1

Note:     Award M1 only if the numerator results from the product of two probabilities.

$= \frac{7}{{31}}{\text{ }}( = 0.2258 \ldots )$     A1

[2 marks]

Both parts were very well done. In part (a), most candidates successfully used a tree diagram.

Both parts were very well done. In part (b), most candidates correctly used conditional probability considerations.