ex4) a study of consumer smoking habits includes 200 married people (54 of whom smoke), 100 divorced people…

ex4) a study of consumer smoking habits includes 200 married people (54 of whom smoke), 100 divorced people (38 of whom smoke), and 50 never - married people (11 of whom smoke). (the u.s. dept. of health and human services). if one subject is randomly selected from this sample, find the probability of getting someone who has never been married or does not smoke.\n\n| | married | divorced | never - married | total |\n|--|--|--|--|--|\n| smokes | 54 | 38 | 11 | 103 |\n| doesnt smoke | 146 | 62 | 39 | 247 |\n| total | 200 | 100 | 50 | 350 |\n\np(a∪b)=p(a)+p(b)-p(a∩b)

ex4) a study of consumer smoking habits includes 200 married people (54 of whom smoke), 100 divorced people (38 of whom smoke), and 50 never - married people (11 of whom smoke). (the u.s. dept. of health and human services). if one subject is randomly selected from this sample, find the probability of getting someone who has never been married or does not smoke.\n\n| | married | divorced | never - married | total |\n|--|--|--|--|--|\n| smokes | 54 | 38 | 11 | 103 |\n| doesnt smoke | 146 | 62 | 39 | 247 |\n| total | 200 | 100 | 50 | 350 |\n\np(a∪b)=p(a)+p(b)-p(a∩b)

Answer

Explanation:

Step1: Identify values for formula

Let event $A$ be the event of selecting a never - married person and event $B$ be the event of selecting a non - smoker. $P(A)=\frac{50}{350}$, $P(B)=\frac{247}{350}$, $P(A\cap B)=\frac{39}{350}$.

Step2: Apply the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$P(A\cup B)=\frac{50}{350}+\frac{247}{350}-\frac{39}{350}=\frac{50 + 247-39}{350}=\frac{258}{350}=\frac{129}{175}\approx0.737$.

Answer:

$\frac{129}{175}$