SOLUTION: Refer to the contingency table shown below. Smoking by Race for Males Aged 18-24 Smoker (S) Nonsmoker (N) Row Total White(W) 290 560 850 Black(B) 30

Algebra ->  Probability-and-statistics -> SOLUTION: Refer to the contingency table shown below. Smoking by Race for Males Aged 18-24 Smoker (S) Nonsmoker (N) Row Total White(W) 290 560 850 Black(B) 30       Log On


   

Question 1158482: Refer to the contingency table shown below.

Smoking by Race for Males Aged 18-24
Smoker
(S) Nonsmoker
(N) Row Total
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000

Click here for the Excel Data File

(a) Calculate the probabilities given below (Round your answers to 4 decimal places.):



i.P(S) 0.3200 0.3200 Correct
ii.P(W) 0.8500 0.8500 Correct
iii.P(S | W) 0.2720 0.2720 Incorrect
iv.P(S | B) 0.0300 0.0300 Incorrect
v. P(S and W) 0.9062 0.9062 Incorrect
vi.P(N and B) 0.1765 0.1765 Incorrect

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Given Data
Smoker (S)Nonsmoker (N)Row Total
White (W)290560850
Black (B)30120150
Column Total3206801000


S = smoker
N = nonsmoker
W = white male aged 18-24
B = black male aged 18-24

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Part i.

P(S) = probability of selecting a smoker
P(S) = (number of smokers)/(number total)
P(S) = 320/1000
P(S) = 0.3200

Answer: 0.3200
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Part ii.

P(W) = probability of selecting a white male
P(W) = (number of white males)/(number total)
P(W) = 850/1000
P(W) = 0.8500

Answer: 0.8500

Nice work on getting parts i and ii correct.
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Part iii.

P(S|W) = probability of selecting a smoker (S) given they are white male (W)
P(S|W) = (number of white male smokers)/(number of white males)
P(S|W) = 290/850
P(S|W) = 0.341176471 which is approximate
P(S|W) = 0.3412 rounded to four decimal places

notice how we only focus on the white male row since we are given the person is a white male.

Answer: 0.3412

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Part iv.

This time we focus on the black male row. Ignore everything else.

There are 30 who smoke out of 150 total
P(S|B) = probability of selecting a smoker (S) given they are a black male (B)
P(S|B) = 30/150
P(S|B) = 0.2000

Answer: 0.2000

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Part v.

This time we consider all males surveyed since we don't have a conditional probability.
P(S and W) = probability of selecting a smoker and a white male
P(S and W) = (number of smokers who are white)/(number of people total)
P(S and W) = 290/1000
P(S and W) = 0.2900

Answer: 0.2900

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Part vi.

P(N and B) = probability of selecting a nonsmoker and a black male
P(N and B) = (number of nonsmokers who are black)/(number of people total)
P(N and B) = 30/1000
P(N and B) = 0.0300

Answer: 0.0300