A commuter has two vehicles, one being a compact car and the other one a minivan. Three times out of four, he uses the compact car to go to work and the remainder of the time he uses the minivan. When he uses the compact car (resp. the minivan), he gets home before 5 : 30 p.m. 75% (resp. 60%) of the time. However, the minivan has air conditioning. Calculate the probability that:
a) he gets home before 5 : 30 p.m. on a given day;
b) he used the compact car if he did not get home before 5 : 30 p.m.;
c) he uses the minivan and he gets home after 5 : 30 p.m.;
d) he gets home before 5 : 30 p.m. on two (independent) consecutive days and
he does not use the same vehicle on these two days.