Problem 1 A particular language certificate is earned after taking three annual exams (type I, II, and III). Candidates who pass an exam are eligible to take the exam for the next level in the following exam session. The pass rates for levels I, II, and III are 0.82, 0.56, and 0.71, respectively. Suppose that 1,836 candidates take the level I exam, 2,720 take the level II exam and 2,244 take the level III exam. Find the probability that: a) a randomly selected candidate passes the exam; c) a randomly selected candidate who passed the exam took one of type II; d) a randomly selected candidate who did not pass the exam took one of type