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A study of consumer smoking habits includes 177 people in the 18-22 age bracket ( 48 of whom smoke), 146 people in the 23-30 age bracket ( 31 of whom smoke), and 81 people in the 31-40 age bracket ( 28 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.A. 0.319B. 0.854C. 0.173D. 0.729

Respuesta :

[tex]\text{The probability of an event occuring = }\frac{number\text{ of required events}}{\text{Total number of events}}[/tex]

From the question,

Age 18 - 22 has 177 people, 48 of whom smoke.

Age 23-30 has 146 people, 31 of whom smoke.

Age 31-40 has 81 people, 28 of whom smoke.

People who do not smoke = (177- 48)+(146-31)+(81-28) = 129 + 115 +53 = 297 people.

People within age 18-22 who do not smoke = 129

Total number of events = 404

[tex]\begin{gathered} p(18-22\text{ or does not smoke) = }\frac{(177+297-129)}{404} \\ p(18-22\text{ or does not smoke)}=\frac{345}{404}=0.853960396 \\ p(18-22\text{ or does not smoke)}\approx0.854 \end{gathered}[/tex]

Hence, option B is the answer.