I have a urn full of M balls with an unknown mix of white and black balls. I draw N balls out (without replacement) and get a particular proportion of white vs black balls. From the looks of it there should be a way for my to calculate the probability the balls I have draw have the same proportion (white vs black) as the balls in the urn.
Am I also able to calculate the probabilities of the various proportions based on what what I've draw?
For example if I have a urn full of 10 balls and I draw out 5 white balls then it would be very unlikely the initial composition of the urn would be 5 white/5 black.