Choose a postmenopausal woman at random. The probability is 0.37 that the woman

Question

Choose a postmenopausal woman at random. The probability is 0.37 that the woman chosen has osteopenia (low but not pathologically low bone density ) and 0.08 that she has osteoporosis (pathologically low bone mineral density).

(a) What is the probability that a randomly chosen postmenopausal woman has a healthy bone density? Please use 2 decimal places.


(b) What is the probability that a randomly chosen postmenopausal woman has some problem with low bone density (osteopenia or osteoporosis)? Please use decimal places.

Explanation / Answer

a) The randomly chosen postmenopausal woman has a healthy bone density if she neither has osteopenia nor has osteoporosis.

Since both cases osteopenia and osteoporosis are disjoint events.

Therefore, the probability that a randomly chosen postmenopausal woman has a healthy bone density is

= 1- (0.37+0.08) = 1-0.45 =0.55

b) The probability that a randomly chosen postmenopausal woman has some problem with low bone density  (osteopenia or osteoporosis) is

= (0.37+0.08) = 0.45

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.