I want to solve a problem with probability

Question

90% of the children in a developing country have caries, 85% have worms and 70% are undernourished. How high is the percentage of children who have all three ailments?

a) At least 70% of the children

b) At least 60% of the children

c) At least 55% of the children

d) At least 45% of the children

Answer 1

Let the people that don't have each of caries, worms, and undernourished be mutually exclusive (this will maximize the probability of their union given the probability of each). Then the number not having at least one of the diseases would be (1 - .9) + (1 - .85) + (1 - .7) = 3 - 2.45 = .55

Then, .45 have all three.

d)