Question 473406: Suppose that a certain college class contains 54 students. Of these, 27 are sophomores, 33 are economics majors, and 10 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a junior and a psychology major?
(b) Given that the student selected is a junior, what is the probability that he is also a psychology major?
Write your responses as fractions.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that a certain college class contains 54 students. Of these, 27 are juniors, 33 are psychology majors, and 10 are neither. A student is selected at random from the class.
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Draw a Venn Diagram with two intersecting circles: J and E
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Let the intersection contain x students.
Equations:
x + J = 27
x + P = 33
J + x + P + 10 = 54
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J = 27-x
P = 33-x
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Substitute and solve for "x":
27-x + x + 33-x = 44
-x = -16
x = 16 (# who are juniors and psych majors)
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(a) What is the probability that the student is both a junior and a psychology major? 16/54
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(b) Given that the student selected is a junior, what is the probability that he is also a psychology major?::: 21/33
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Write your responses as fractions.
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Cheers,
stan H.
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