Math and probability

Question

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.)

Answer 1

Probability of failing first time is 39%, second time is 37% and 3rd time is 58%.

Since the 3 chances are independent events then the probability of failing all 3 times is:

0.39 * 0.37 * 0.58 = 0.08 = 8%