## Question

At a nursing college, 80 % of incoming students are female. College records show that 70 % of the incoming females graduate and 90 % of the incoming males graduate. A student who graduates is selected at random. Find the probability that the student is male, giving your answer as a fraction in its lowest terms.

**▶️Answer/Explanation**

## Markscheme

\({\text{P }}M|G = \frac{{{\text{P}}(M \cap G)}}{{{\text{P}}(G)}}\) *(M1)*

\( = \frac{{0.2 \times 0.9}}{{0.2 \times 0.9 + 0.8 \times 0.7}}\) *M1A1A1*

\( = \frac{{0.18}}{{0.74}}\)

\( = \frac{9}{{37}}\) *A1*

*[5 marks]*

## Examiners report

Most candidates answered this question successfully. Some made arithmetic errors.

## Question

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.

**▶️Answer/Explanation**

## Markscheme

*(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]*

## Examiners report

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