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) About Me  (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(52803) About Me  (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 = %2824%2B56%29%2F200 = 80%2F200 = 40%2F100 = 2%2F5 = 0.4 = 40%.



(b)  P = %28%2824%2B56%29+%2B+38%29%2F200 = 118%2F200 = 59%2F100 = 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 = 38%2F%2838%2B82%29 = 38%2F80 = 19%2F40 = 0.475 = 47.5%.


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


All questions are answered.