a Given the table below if one person from the study is rand

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.

Solution

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]