Question

Choose a postmenopausal woman at random. The probability is 0.46 that the woman chosen has osteopenia (low but not pathologically low bone density ) and 0.09 that she has osteoporosis (pathologically low bone mineral density. Assume that a woman can't have both diseases simultaneously. (a) What is the probability that a randomly chosen postmenopausal woman has a healthy bone density

Answer 1

The probability that a randomly chosen postmenopausal woman has a healthy bone density is 0.45.

Explanation:

Probability of the postmenopausal woman having osteopenia = 0.46

Probability of the postmenopausal woman having osteoporosis = 0.09

Probability of having either osteopenia or osteoporosis = 0.55 (0.46 + 0.09).

Therefore, the probability that the postmenopausal woman does not have either osteopenia or osteoporosis, which is the same as having a healthy bone density = 0.45 (1 - 0.55).