Probabilty of two stage events (man & women) ; (smokers & nonsmokers) A person is selected at random from a population that has the following characteristics: 65% of the people are men; the others are women 12% of the men are smokers 7% of the women are smokers i) Find the chance that the selected person is a man or a non-smoker P(man or a non-smoker)= P(man) + P(non-smoker) - P(man of non-smoker) inclusion P(man)=0.65 Given P(man-non-smoker)= 0.65*(1-0.12)=0.65*0.88=0.572 P(women)=0.35 given P(women-nonsmoker)=0.35*(1-0.07)=0.35*0.93=0.3255 P(non-smoker)=(p(man non-smoker + women non-smoker)=0.572+0.3255=0.8975 p(man or non-smoker)=P(man + non-smoker)-P(man of non-smoker)= (0.65+0.8975)-(0.572)=0.9755 is this method correct approach?

Sounds good to me. Alternatively, you may also go this way: \begin{align} P(\mbox{man or non-smoker}) & = P(\mbox{man})+P(\mbox{woman and non-smoker}) \\\ & = 0.65 + 0.35 \times 0.93 \\\ & = 0.9755. \end{align}