(Solved): Consider two urns. Urn I contains 3 white and 4 black balls. Urn II contains 2 white and 6 black b ...

Consider two urns. Urn I contains 3 white and 4 black balls. Urn II contains 2 white and 6 black balls. (a) Assuming equiprobability, what is the probability of picking a white ball from Urn I? What is the probability of picking a white ball from Urn II? (b) Now pick a ball randomly from Urn I and place it in Urn II. Next you pick a ball randomly from Urn II. What is the probability that the ball you picked from Urn II is black? (c) Now pick an Urn at random, each of the two urns picked with a probability of \( \frac{1}{2} \). Then in a second step pick a ball at random from your chosen Urn. If the ball you picked is black, what is the probability that in the first step you picked Urn I in the first step?