SOLUTION: Suppose that a certain college class contains 58 students. Of these, 25 are sophomores, 34 are history majors, and 11 are neither. A student is selected at random from the class.

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Question 633163: Suppose that a certain college class contains 58 students. Of these, 25 are sophomores, 34 are history majors, and 11 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 she is also a sophomore?
Write your responses as fractions.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

 58 students

25 are sophomores,   

34 are history majors

11 are neither.

 58-11 = 47

 59 - 47 =  12

12, both soph and history majors

13 sophmores only

22 history majors only

P(soph & H maj) = 12/58 = 6/29

P(soph, given H maj) =   = 12/22 = 6/11  |P(A|B) = P(A and B)/P(B) 

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