SOLUTION: 60 students pass the maths exam and 50 pass the english exam. 10 students pass in neither of the exams and 50% passed both the exams. What is the probability that a student selecte

Algebra ->  Probability-and-statistics -> SOLUTION: 60 students pass the maths exam and 50 pass the english exam. 10 students pass in neither of the exams and 50% passed both the exams. What is the probability that a student selecte      Log On


   

Question 388799: 60 students pass the maths exam and 50 pass the english exam. 10 students pass in neither of the exams and 50% passed both the exams. What is the probability that a student selected at random passed in maths?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let N = total # of students.
Then N%2F2 = # students who passed BOTH math and english,
50+-+N%2F2 = # students who passed english but not math, and
60+-+N%2F2 = # students who passed math but not english.
Hence
50+-+N%2F2+%2B+N%2F2+%2B+60+-+N%2F2+%2B+10+=+N,
120+-+N%2F2+=+N,
120+=+3N%2F2, or N = 80, the total number of students.
Therefore the probability that a student selected at random passed in maths is 60/80, or 3/4.