b Given that the student selected is a history major what is

(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.)

Solution

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