Jenny goes to school by bus every day. When it is not raining, the probability that the bus is late is $\frac{3}{{20}}$. When it is raining, the probability that the bus is late is $\frac{7}{{20}}$. The probability that it rains on a particular day is $\frac{9}{{20}}$. On one particular day the bus is late. Find the probability that it is not raining on that day.

     (A1)

${\text{P}}(R' \cap L) = \frac{{11}}{{20}} \times \frac{3}{{20}}$     A1

${\text{P}}(L) = \frac{9}{{20}} \times \frac{7}{{20}} + \frac{{11}}{{20}} \times \frac{3}{{20}}$     A1

${\text{P}}(R'|L) = \frac{{{\text{P}}(R' \cap L)}}{{{\text{P}}(L)}}$     (M1)

$= \frac{{33}}{{96}}{\text{ }}\left( { = \frac{{11}}{{32}}} \right)$     A1

[5 marks]

This question was generally well answered with candidates who drew a tree diagram being the most successful.