Groups of dice probability

#1
I am new to Statistics and this was a homework that was given to us. I was able to come up with the answer during the class last week, but my professor said that it was an indirect method and wanted me to revisit this problem. If some one could help me with this problem and explain it, I would really appreciate it. Thanks again

Code:
Assume that we have two groups of dice. 
For half of them, call them Type I dice, ace (the side with one dot) comes up 30% of the time. 
For the other half, call them Type II dice, ace (the side with one dot) comes up 60% of the time.  
If a die is selected, rolled, and an ace comes up, what is the probability it is Type I ace?  
What is the probability it is Type II ace?