SOLUTION: An investigator wishes to study a particular environmental factor, namely, the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their

You are given a general info that

(1) if both the mother and father are current smokers 
    then the probability of their offspring having asthma is 0.15 


(2) if the mother is a current smoker and the father is not 
    then the probability of their offspring having asthma is 0.13. 


(3) if the father is a current smoker and the mother is not, 
    then the probability of their offspring having asthma is 0.05 


(4) if neither parent is a current smoker, 
    then the probability of their offspring having asthma is 0.04.


Next, you are given an additional portion of information:

    (a) The probability that the father is a current smoker is 0.5. 
    (b) If the father is a current smoker then the probability that the mother is a current smoker is 0.6;
    (c) whereas if the father is NOT a current smoker then the probability that the mother is a current smoker is 0.2.


From this additional info, it is easy to deduce that

    P(F is a smoker, M is a smoker)     = 0.5*0.6 = 0.3;    (a)

    P(F is a smoker, M is a not smoker) = 0.5*0.4 = 0.2;    (b)

    P(F is not a smoker, M is a smoker) = 0.5*0.2 = 0.1.    (c)


From these occurrences (a), (b) and (c), we deduce that

    P(F is not a smoker, M is not a smoker) = the COMPLEMENT to (a), (b), (c) = 1 - 0.3 - 0.2 - 0.1 = 0.5   (d).


Finally, we combine (1) with (a); (2) with (c), (3) with (b) and (4) with (d), and we get

    P(the offspring will have asthma) = 0.15*0.3 + 0.13*0.1 + 0.05*0.2 + 0.04*0.1 = 0.072.


ANSWER. Based on given info, the probability that the offspring will have asthma is 0.072.