An urn contains 1 red ball, 1 yellow ball and 1 blue ball. A ball is randomly selected. a) Find the probability distribution for the number of yellow balls. b) Find the expected value and variance for...

Extracted text: An urn contains 1 red ball, 1 yellow ball and 1 blue ball. A ball is randomly selected. a) Find the probability distribution for the number of yellow balls. b) Find the expected value and variance for the number of yellow balls. Now, consider three urns. Urn 1 contains 1 red ball, 1 yellow ball and 1 blue ball. Urn 2 contains 1 red ball, 2 yellow balls and no blue ball. Urn 3 contains 1 red ball, no yellow ball and 2 blue balls. A random experiment is now performed in two steps. First you select an urn and then a ball from the selected urn. Urn 1 is chosen with the probability p1 = 1 urn 2 is chosen with the probability p2 = 3' 3' and urn 3 is selected with the probability p3 =; c) Find the probability distribution for the number of yellow balls and calculate the expected value and variance. (The answer is the same as in question b) a fact that contradicts intuition.)