2. According to the Center for Disease Control (CDC) there were approximately 24
ID: 3207011 • Letter: 2
Question
2. According to the Center for Disease Control (CDC) there were approximately 241,721,854 adults (18 years or older) in the U.S. in 2015 out of which 36,500,000 were current smokers. Half of the U.S. adults in 2015 were women and 13.6% of adult women were current smokers. Please answer the following questions based on the information given in this problem.
a. What is the probability that a random U.S adult will be both a smoker and a man?Please show the necessary work.
b. If a 30 years old U.S. resident happens to be a non-smoker, what is the probability that he is a man? Please show the necessary steps. [3 points]
c. What is the probability that a random U.S adult will be a non-smoker or a man? Please show the necessary work. [2 points]
d.What is the probability that a random U.S adult will be neither a smoker nor a woman? Show the necessary work. [2 points]
e. Are being a smoker and being a women independent events for a U.S adult? Please show how you arrived at your answer.
Explanation / Answer
No of Adults in US = 241,721,854
No fo smokers = 36,500,000
Assuming man and woman to be the only genders here ,
No of women =120860927
No of men = 120860927
Given 13.6% of adult women are smokers = 13.6% of 120860927 = 16437086
Therefore Number of Male Smokers = 36500000 - 16437086 = 20062914
Number of males who dont smoke = 120860927-20062914 =100798013
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a) Probability of a random adult chosen to be both a smoker and a man
= No of ways a man smoker can be chosen / Total no of ways an adult can be chosen
=20062914C1/241721854C1
=0.083
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b)Since number of 30 yeard old is not given we can solve it just to assume he is adult and proceed ,
If he is a non smoker = No of ways of choosing a non smoker man = 100798013C1
No of ways of choosing an adult =241721854C1
Therefore Probability = 100798013C1/241721854C1 =0.417
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c) Total Probability = P(non-smoker) + P(Man)
= P (non-smoker) = Total Number of non smoker / Total Population = 100798013/241721854 =0.417
=P(man)= No of men / Total adults = 120860927/241721854 = 0.5
Therefore = 0.417 + 0.5 = 0.917
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d)Total Probability = Probability of neither a smoker nor a woman = Probability of a man who smokes =
This is equal to a which is 0.083
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