An applicant has a 0.26 probability of passing a test when they take it for the first time, and if they pass it they can move on to the next stage. However, if they fail the test the first time, they must take the test a second time, and when an applicant takes the test for the second time there is a 0.43 chance that they will pass and be allowed to move on to the next stage. The applicant is rejected if the test is failed on the second attempt.
(a) What is the probability that an applicant moves on to the next stage but needs two attempts at the test?
(b) What is the probability that an applicant moves on to the next stage?
(c) If an applicant moves on to the next stage, what is the probability that they passed the test on the first attempt?