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.

${\text{P }}M|G = \frac{{{\text{P}}(M \cap G)}}{{{\text{P}}(G)}}$     (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]

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