The University of Metropolis requires its students to pass a

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.)

Solution

For the sake of understanding, consider there are 100 students.

If 61% pass in 1st attempt, then 61 clear and 100 - 61 = 39 try again.

Of the 39, 63% pass meaning 39(100 -63)% = 14 fail and re-take one final time

42% of those pass and the remaining 58% fail = 14*(1 -.42) = 7.8 = 8 students.

8 of the original 100 are not allowed to graduate = 8%

We can now formalize and write down a formula

Let x be no of students. Then % failing to graduate = x(1-.61)(1-.63)(1-.42)/x = .39*.37*.58 = .0837 = 8.37%

Answer: 8%