So the question is as follows:
X need to pass four out of five separate tests for certification. Assume that the tests are equally difficult, and that the performance on separate tests are independent.
If the probability of failing each separate test is p = 0.15, then what is the probability of failing certification?
So I tried the binomial distribution, effectively seeing what are the chances of passing at least 4 exams (and failing one) and then adding the probability of passing all 5 exams.
This yields an overall failure probability of just over 0.16. Is this a correct approach?
Thank you!
Best Answer
Yeah , your approach is correct.
Look, Probability of passing certification = (0.85)^5 + 5*C1*(0.15)*(0.85)^4
(As in this case he will clear all subjects or will be failed only in a single subject)
So Probability of passing certification = 0.4437+ 0.3915 = 0.83521
Thus required probability of failing certification = 1 - 0.83521 = 0.16479