If 15% of adult females smoke..

Question

An ectopic pregnancy is one where gestation occurs outside the uterus. The condition is twice as likely for a female who smokes than for one who is a nonsmoker. If 15% of Adult females smoke, what percentage of ectopic pregnancies involve a female who smokes?

Answer 1

By definition of conditional probability,

P (smoke|ectopic) = P (ectopic|smoke) x P (smoke) / P (ectopic)

 

By law of total probability,

P (ectopic) = P (ectopic|smoke) × P (smoke) + P (ectopic|not smoke) × P (not smoke)

 

Suppose y = P (ectopic|not smoke). Then from the problem, we know P(ectopic|smoke) = 2 × P (ectopic|not smoke) = 2y. Substitute this into the above two equations:

 

P(ectopic) = 2y × 0.15 + y × 0.85 = 1.15y

 

P (smoke|ectopic) = 2y × 0.15 / 1.15y = 6/23

 

 

 

Answer 2

15%

Check the problem. The problem provides the answer.