Final answer:
The probability that no one in a family of six will be hospitalized in a certain year is 49.2%.
Step-by-step explanation:
To find the probability that no one in a family of six will be hospitalized in a certain year, we can use the concept of independent events. Since the probability of being hospitalized is 0.12, the probability of not being hospitalized in one year is 1 - 0.12 = 0.88. We can assume that the hospitalization of each family member is independent of the others, so the probability that no one in the family will be hospitalized is (0.88)^6 = 0.492 = 49.2%.