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.

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