F is the event that some colonist gets the flu, and this is given as 0.1 (10%). Also notice that E and F are mutually exclusive events (someone can't be both vaccinated and not vaccinated at the same time). So, we use the first principle:
First, since 90% of the colonists are vaccinated and, of those, 3% get the flu, the percentage of colonists who are vaccinated and get the flu is 3% of 90%, or 2.7%. Thus,
Next notice that EF is the event that some colonist gets the flu, and this is given as 0.1 (10%). Also notice that E and F are mutually exclusive events (someone can't be both vaccinated and not vaccinated at the same time). So, we use the first principle:
F) = P(E) + P(F)
Therefore,
P(F) =.1 - .027 = .073.
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