SOLUTION: A college has 64 students. 36 are sophomores, 39 mathematic majors and 6 are neither. A student is picked at random from the class. a. What is the probability that the studen

Question 136403: A college has 64 students. 36 are sophomores, 39 mathematic majors and 6 are neither. A student is picked at random from the class.
a. What is the probability that the student is both a sophomore and a math major?
b. If the student is a sophomore, what is the probability that he is also a math major? Write yor response as fractions. Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A college has 64 students. 36 are sophomores, 39 mathematic majors and 6 are neither. A student is picked at random from the class.
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6 are neither, so 58 either or both.
Let "x" be the number that are both.
Them 36 + 39-x = 58
x = 17 (# who are sophomore and math major)
36-17= 19 (# who are sophomore and not math major)
39-17= 22 (# who are math major and not sophomore)
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a. What is the probability that the student is both a sophomore and a math major?
P(soph AND math) = 17/64
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b. If the student is a sophomore, what is the probability that he is also a math major? Write yor response as fractions.
P(math major|soph) = 17/39
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Cheers,
Stan H.
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