Question

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.

	married	divorced	never - married	total
doesnt smoke	146	62	39	247
total	200	100	50	350

p(a∪b)=p(a)+p(b)-p(a∩b)

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:

$\frac{129}{175}$