Question 58909: A standard admissions test is given at three locations every year. One thousand students took the exam at location A, six hundred at location B, and four hundred at location C. The percentages of students from locations A, B, and C who passed the exam were 70%, 68%, and 77% respectively. One student is selected at random from all of those who took the exam.
a) What is the probability that the student passed the exam?
b) If the selected student passed the exam, what is the probability that the student took the test at location B?
c) What is the probability that the student took the exam at location C and failed?
d) Calculate the probability that the student failed the exam.
e) If the selected student failed the exam, what is the probability that the student took the exam at location A?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A standard admissions test is given at three locations every year. One thousand students took the exam at location A, six hundred at location B, and four hundred at location C. The percentages of students from locations A, B, and C who passed the exam were 70%, 68%, and 77% respectively. One student is selected at random from all of those who took the exam.
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I drew a contingency table with rows A, B, and C and columns Passed and Failed
I then filled in the boxes and the row and column totals. I would recommend
you do that for yourself.
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a) What is the probability that the student passed the exam?
Number who passed is 0.7(1000)+0.68(600)+0.77(400)=1416
Total number of students is 2000
Prob (a randomly selected student passes)= 1416/2000=0.708
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b) If the selected student passed the exam, what is the probability that the student took the test at location B?
P(at B|passed) = 408/1416=0.288
c) What is the probability that the student took the exam at location C and failed?
92/400=0.23
d) Calculate the probability that the student failed the exam.
1-0.708 = 0.292
e) If the selected student failed the exam, what is the probability that the student took the exam at location A?
300/584=0.513698...
Cheers,
Stan H.
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