Question

A study of consumer smoking habits includes 194194 people in the​ 18-22 age bracket ​(4848 of whom​ smoke), 142142 people in the​ 23-30 age bracket ​(3333 of whom​ smoke), and 8989 people in the​ 31-40 age bracket ​(2020 of whom​ smoke). If one person is randomly selected from this​ sample, find the probability of getting someone who is age​ 18-22 or does not smoke.

Answer 1

Answer:

0.8753

Step-by-step explanation:

Total Population=194+142+89=425

Population of those who smoke=48+33+20=101

Population of non smokers=425-101=324

Population of those in 18-22 bracket=194

Population of nonsmoker's in 18-22 age bracket=194-48=146

Probability of getting someone who is age​ 18-22 = [TeX]\frac{194}{425}[/TeX]

Probability of getting someone who does not smoke = [TeX]\frac{324}{425}[/TeX]

Let the event that the person is in age bracket 18-22 be A

Let the event that the person does not smoke be B

Therefore, the probability of getting someone who is age​ 18-22 or does not smoke

=Probability of getting someone who is age​ 18-22 + Probability of getting someone who does not smoke - Probability of those who do not smoke and are in the age bracket 18-22

P(A or B)=P(A)+P(B)-P(A and B)

=[TeX]\frac{194}{425}+\frac{324}{425}-\frac{146}{425}[/TeX]

[TeX]=\frac{194+324-146}{425}=\frac{372}{425}=0.8753[/TeX]