Question

A study of consumer smoking habits includes 168 people in the 18-22 age bracket (48 of whom smoke), 131 people in the 23-30 age bracket (36 of whom smoke), and 99 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.

Group of answer choices

0.839

0.302

Answer 1

Solution :

The data can be represented in the tabular form as follows :

	18 - 22	23 - 30	31 - 40	Total
Smoke	48	36	28	112
Do not smoke	120	95	71	286
Total	168	131	99	398

We have to find P(age 18-22 or dose not smoke).

P(age 18-22 or does not smoke) = P(age 18-22) + P(does not smoke) - P(age 18-22 and does not smoke)

P(age 18-22) = number of people aged 18-22/Total number of people

P(age 18-22) = 168/398

P(does not smoke) = number of people who don't smoke/Total number of people

P(does not smoke) = 286/398

P(age 18-22 and does not smoke) = Number of 18-22 aged people who do not smoke/Total number of people

P(age 18-22 and does not smoke) = 120/398

Hence,

P(age 18-22 or does not smoke) = (168/398) + (286/398) - (120/398)

P(age 18-22 or does not smoke) = 334/398

P(age 18-22 or does not smoke) = 0.839

Hence, the probability of getting someone who is age 18-22 or does not smoke is 0.839.

Please rate the answer. Thank you.