Part a)
P(junior) = (number of juniors)/(number total)
P(junior) = 235/705
P(junior) = 1/3 exactly
P(junior) = 0.33333 approximately
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Part b)
P(freshman and LG) = (number of freshman who have LG)/(number total)
P(freshman and LG) = 70/705
P(freshman and LG) = 14/141 exactly
P(freshman and LG) = 0.09929 approximately
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Part c)
n(junior) = number of juniors = 235
n(samsung) = number of people who have samsung = 274
n(junior and samsung) = number of juniors who have samsung = 93
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n(junior or samsung) = n(junior)+n(samsung)-n(junior and samsung)
n(junior or samsung) = 235+274-93
n(junior or samsung) = 416
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P(junior or samsung) = n(junior or samsung)/n(total)
P(junior or samsung) = 416/705 exactly
P(junior or samsung) = 0.59007 approximately
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Part d)
n(sophomore and apple) = number of sophomores who have apple
n(sophomore and apple) = 80
n(apple) = number of students who have apple
n(apple) = 261
P(sophomore | apple) = n(sophomore and apple)/n(apple)
P(sophomore | apple) = 80/261 exactly
P(sophomore | apple) = 0.30651 approximately
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Part e)
define the events
A = junior who has apple
B = junior who has samsung
C = person is a junior
n(A or B) = number of juniors who have apple or samsung
n(A or B) = n(A) + n(B) ... A and B assumed mutually exclusive
n(A or B) = 87+93
n(A or B) = 180
n(C) = 235
P( (Apple or Samsung) | Junior ) = n(A or B)/n(C)
P( (Apple or Samsung) | Junior ) = 180/235
P( (Apple or Samsung) | Junior ) = 36/47 exactly
P( (Apple or Samsung) | Junior ) = 0.76596 approximately