SOLUTION: A researcher wanting to investigate the prevalence of smoking among teens selected a random sample of 200 teens and asked whether or not they smoked. This information is recorded i

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Question 1142523: A researcher wanting to investigate the prevalence of smoking among teens selected a random sample of 200 teens and asked whether or not they smoked. This information is recorded in the following table:
Yes No
Male 38 82
Female 24 56
a) What is the probability of randomly selecting a teen that is female?
b) What is the probability of randomly selecting a teen that is female and smokes?
c) What is the probability of randomly selecting a teen that smokes given that he is
male?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


a) From the basic definition of probability,
      number of females
  --------------------------
  total number in the sample

b) From the same definition,
   number of females who smoke
  -----------------------------
   total number in the sample

c) With the condition "given that he is a male", the denominator of the probability fraction is only the number of males in the sample:
    number of males who smoke
   ---------------------------
     total number of males
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.

First,  I checked that the sum of all numbers in the Table is  200 :   38 + 82 + 24 + 56 = 200.   ! Correct ! 


(a)  P =  =  =  =  = 0.4 = 40%.



(b)  P =  =  =  = 0.59 = 59%.


         To the total number of female teens add the number of smoking male teens;  then relate the sum to 200.


         Very simple and does not require additional explanations.



(c)  P =  =  =  = 0.475 = 47.5%.


     It looks OBVIOUS to me, since in this case you, actually, select among 80 male teens.


All questions are answered.



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