Question 263647: The University of Metropolis requires its students to pass an examination in college-level mathematics before they can graduate. The students are given three chances to pass the exam; 61% pass it on their first attempt, 63% of those that take it a second time pass it then, and 42% of those that take it a third time pass it then.
What percent of the students are not allowed to graduate because of their performance on the exam? (Round the answer to the nearest whole number.)
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! The University of Metropolis requires its students to pass an examination in college-level mathematics before they can graduate. The students are given three chances to pass the exam; 61% pass it on their first attempt, 63% of those that take it a second time pass it then, and 42% of those that take it a third time pass it then.
What percent of the students are not allowed to graduate because of their performance on the exam? (Round the answer to the nearest whole number.)
Since 61% pass the exam the 1st time, then 39% (100% - 61%) failed the 1st time
Since 63% of those who fail the 1st time pass the exam the 2nd time, then 25% (63% of 39%) of those who took it a 2nd time passed it, and 14% (39% - 25%) failed it the 2nd time
Since 42% of those who fail the 2nd time pass the exam the 3rd time, then 6% (42% of 14%) of those who took it a 3rd time passed it, and 8% (14% - 6%) failed it the 3rd time.
This means that  % of the students will not be allowed to graduate as this percentage of students have failed the exam for a 3rd time.
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