The probabilities of the weather being fine, raining, or snowing are respectively 1/2, 1/3, and 1/6. The probabilities that a student arrives on time for school under each of these conditions is 3/4,...

The probabilities of the weather being fine, raining, or snowing are respectively 1/2, 1/3, and 1/6. The probabilities that a student arrives on time for school under each of these conditions is 3/4, 2/5, and 3/10 respectively. What is the probability that:
a. the student arrives at school on time on any given day;
b. if the student is late, it was raining?