Urn I contains 25 white and 15 black balls. Urn II contains 15 white and 25 black balls. An urn is selected at random and five balls are drawn randomly from this urn without replacement. If exactly five of these balls are white, what is the probability that the balls came from Urn I?
So my question derives from the "without replacement" part of the question. I am assuming all five balls are drawn from a urn at the same time rather than one by one? But then it confuses me why they would throw in "without replacement" if you would draw them all at the same time. Anyone have insight on whether it is one-by-one or not?
Given that they are drawn at the same time I get: P(U1|W) = P(U1 AND W)/P(W) which turns into P(W|U1)(P(U1)/ (P(W|U1)P(U1) + P(W|U2)P(U2)) Where W: the five balls drawn are white Ui: Urn i is choosen
is this correct?