Use the following events:

E: the event that a colonist was exposed through vaccination; P(E) = 0.9
F: the event that a colonist was not vaccinated and exposed through infection; P(F) = 0.073
(from the next-to-last question)

The event that a colonist was exposed to the virus either by vaccination or by getting the flu is then EF. Since these are mutually exclusive,

P(EF) = P(E) + P(F) = 0.9 + 0.073 = 0.973.