There are A, B, and C types of problem set, and each type of problem set contains 3000, 2000, 5000 problems, respectively. Suppose you can solve A-type problem with 90% probability, B-type problem with 20% probability, and C-type problem with 60% probability. To pass graduation exam, you must solve both of two questions randomly chosen from the total problem set (out of 10,000 problems). Answer the following questions:

1) What is the probability that you pass the graduation exam?

2) What is the probability that you have solved one or more A-type questions when you passed the exam?