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.