Suppose a game show called Bayesian Boxes has the contestant sample one marble from a box and guess what type of box it is. When the contestant picks a box, the chance of each box type for this round is as follows: Type A: 75%, Type B: 20%, and Type C: 5%
The chance of drawing a red marble from Type A is 2%, from Type B is 25%, and from Type C is 98%.
The contestant selects a box and draws a marble. What is the chance of drawing a red marble? (Give the exact decimal answer.)
If the contestant does draw a red marble, what is the chance it came from box Type C? (Give the decimal answer rounded to at least four places.)