Here is my question I could not figure it out by myself:

There are two types of bags H and R in a single box (black box and you can't see through!). The number of the two types of bags are more than 10,000 that can be treated as infinite. In bag type H there are red (3/4) and white (1/4) balls (infinite number), in bag type R there are only white balls (also infinite number). Also I know the chance to pick bag type H is 2/3 and bag R is 1/3 from the box. Now I have randomly picked 16 balls from one bag, the 16 balls are all white. How much is the probability that these 16 balls are from bag of type R? How much is the probability that all these balls are from bag of type H.

This seems to me a Bayesian posterior probability question, but not quite sure. Intuitively these balls must be from a R type bag, as the chance to get them from the bag of type H is very low, but I need a formal calculation to address this question which is quite common in classic probability. Any help is appreciated!

Thanks!

Yifang