(b) Given that the student selected is a history major, what is the probability
ID: 3409168 • Letter: #
Question
(b) Given that the student selected is a history major, what is the probability that he is also a sophomore?
(If necessary, consult a list of formulas.)
(a)
(b)
Suppose that a certain college class contains students. Of these, are sophomores, are history majors, and are neither. A student is selected at random from the class.(a) What is the probability that the student is both a sophomore and a history major?(b) Given that the student selected is a history major, what is the probability that he is also a sophomore?
Write your responses as fractions.(If necessary, consult a list of formulas.)
Explanation / Answer
Let the intersection contain x students.
Equations:
x + S = 36
x + H = 36
S + x + H + 9 = 65
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S=36-x
H=36-x
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Substitute and solve for "x":
36-x + x + 36-x = 56
-x = -16
x = 16 (# who are Sophomores and history majors)
(a) probability that the student is both a sophomore and a history major = 16/65
(b) P(sophomore|history) = P(sopho and histo)/P(histo) = (16/65)/(36/65) = 16/36 = 4/9
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