a. Given the table below, if one person from the study is randomly selected, fin

Question

a. Given the table below, if one person from the study is randomly selected, find the probability the person is over 40 or drinks lemon-lime.

b. Given the table below, if one person from the study is randomly selected, find the probability the person drinks cola if they are over 40.

c.Given the table below, if three people from the study are randomly selected without replacement, find the probability all 3 are under 21 and drink Cola

d. For the table below, if one person from the study is randomly selected, find the probability the person is under 21 given that they drink root beer.

Age Cola Root beer Lemon-lime Total Under 21 40 25 20 85 21 to 40 35 20 30 85 Over 40 20 30 35 85 Total 95 75 85 255

Explanation / Answer

a)

P(over 40 or drinks lemon-lime) = (20+30+35+30+20)/255 = 0.529411765 [ANSWER]

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b)

P(cola|over 40) = 20/85 = 0.235294118 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    255      
K = number of successes in the population =    40      
n = sample size =    3      
x = number of successes in the sample =    3      
          
Thus,          
          
P(   3   ) =    0.003617544 [ANSWER]

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d)

P(under 21|root beer) = 25/75 = 0.33333333 [ANSWER]

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