In Ageing Research Reviews (May 2014), nutritionists published a study of the health issues faced by aging adults. Three of the most common health conditions are obesity (high body fat mass), osteoporosis (low bone mineral density in neck and spine), and sarcopenia (low skeletal muscle mass index). The researchers provided names for aging adults who suffer from one or more of these conditions. These are shown in the accompanying Venn diagram. Statistics from the CDC are used to estimate the following probabilities:
P(Obesity) = .35
P(Osteoporosis) = .30
P(Sarcopenia) = .15
P(Osteopenic Obesity) = .01
P(Osteopenic Sarcopenia) = .03
P(Sarcopenic Obesity) = .05
P(Osteo-sarcopenic Obesity) = .02

a. Find the probability that an adult suffers from both obesity and sarcopenia.
b. Find the probability that an adult suffers from either obesity or sarcopenia?