The length of time for students to complete a 1-hour timed standardized mathematics test has probability density function f (t) = 1.5t² + t, 0 ≤ t ≤ 1 where t is the time in hours. Find the probability that the time it takes a randomly selected student to complete the test is

(a) More than 45 minutes.

(b) More than 30 minutes given that it is less than 45 minutes.