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17 April, 16:19

A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age bracket (D of whom smoke), and E people in the 31-40 age bracket (F of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.

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  1. 17 April, 16:21
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    The correct question is:

    A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes

    Answer:

    The probability of getting someone who is age 23-30 or smokes = 0.575

    Step-by-step explanation:

    We are given;

    Number consumers of age 18 - 22 = 167

    Number of consumers of ages 22 - 30 = 148

    Number of consumers of ages 31 - 40 = 85

    Thus, total number of consumers in the survey = 167 + 148 + 85 = 400

    We are also given;

    Number consumers of age 18 - 22 who smoke = 59

    Number of consumers of ages 22 - 30 who smoke = 31

    Number of consumers of ages 31 - 40 who smoke = 23

    Total number of people who smoke = 59 + 31 + 23 = 113

    Let event A = someone of age 23-30 and event B = someone who smokes. Thus;

    P (A) = 148/400

    P (B) = 113/400

    P (A & B) = 31/400

    Now, from addition rule in sets which is given by;

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

    We can now solve the question.

    Thus;

    P (A or B) = (148/400) + (113/400) - (31/400)

    P (A or B) = 230/400 = 0.575
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