In an ectopic pregnancy, the fertilized egg attaches someplace other than the ma

Question

In an ectopic pregnancy, the fertilized egg attaches someplace other than the main uterine cavity (e.g. fallopian tubes, cervix, ovary). This type of pregnancy can be life threatening or have negative consequences on future pregnancies if left untreated. One risk factor associated with ectopic pregnancies is smoking. In pregnant smokers, the risk of an ectopic pregnancy is 4 times the risk of an ectopic pregnancy in pregnant non-smokers. If only 12% of women of childrearing age are smokers, then what proportion of women having ectopic pregnancies are smokers?

Explanation / Answer

Here, we are given that:

P( ectopic | smokers ) = 4P( ectopic | non smokers )

Let P( ectopic | non smokers ) = K, then P( ectopic | smokers ) = 4K

And, we also are given here that: P( smokers ) = 0.12,

Therefore, P( non smokers ) = 1 - P( smokers ) = 1 - 0.12 = 0.88

Now using law of total addition, we get:

P( ectopic ) = P( ectopic | smokers )P( smokers ) + P( ectopic | non smokers ) P( non smokers )

P( ectopic ) = 0.12*4K + 0.88*K = 1.36K

Now given that a women is ectopic, probability that she is a smoker is computed here as:

P( smoker | ectopic) = P( ectopic | smokers )P( smokers ) / P( ectopic )

P( smoker | ectopic) = 0.12*4K / 1.36K = 0.3529

Therefore 0.3529 is the required probability here.

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