Suppose I put 10 red balls and 40 blue balls into a bucket. Then I put another 50 balls in that I drew at random from a set of 100 red balls and 100 blue balls.
At this point I believe the probability of drawing a red ball from the bucket is 0.35 and the probability of drawing a blue ball is 0.65. Is this correct?
Now if I actually draw a ball, and it is red, how do I calculate the probability of drawing each color on the second ball? And similarly if the first ball were blue?
This is not homework - it is an attempt to create a simple analogy from a more convoluted problem I am trying to solve.