SOLUTION: Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class.

Question 266210: Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a freshman and an economics major?
(b) Given that the student selected is a economics major, what is the probability that she is also an freshman?
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 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a freshman and an economics major?
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P(frosh and econ) = P(frosh) + P(econ) - P(frosh or econ)
= 36/65 + 34/65 - (65-9)/65
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= (36 + 34 - 56)/65
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= 14/65
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(b) Given that the student selected is a economics major, what is the probability that she is also an freshman?
P(frosh|econ) = P(frosh and econ)/P(econ) = (14/65)/(34/65) = 14/34 = 7/17
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Cheers,
Stan H.

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