A number of answers were submitted to this problem (see below). The winner is Alex Cole, with commendations to Khadija Khairoun and Steve Baker. All of the competitors identified that the issue lies in the combination of probabilities that are not independent. Unfortunately Alex's answer, which used Bayes's Theorem, has too much mathematics to be easily turned into HTML so I'm not posting it here. The problem was taken from Raymond Smullyan's book The Riddle of Sheherazade and Other Amazing Puzzles.
Greenwich Maths Challenge 2 will be published here on Monday 7 December at 8pm (or as soon after as I remember).
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