A study was conducted to investigate the association between bone mineral density and the risk of fracture in elderly individuals. Bone mineral density scans of the ankle were taken, and bone mineral density less than or equal to 0.57 was classified as low. Individuals were also assessed for whether they had a fracture. Let B represent the event that an individual had low bone mineral density, and let F represent the event that the individual had a fracture. It was found that 80% of the sample did not have a fracture; 65% of the sample had low bone mineral density; and 28% of the sample both did not have a fracture and did not have low bone mineral density. a. Find the probability that an individual did have a fracture.

b. Find the probability that an individual both had a fracture and had low bone mineral density.

c.Find the probability that an individual had low bone mineral density given that they had a fracture.

d.Are low bone mineral density and fracture independent?