An urn initially contains two black balls and two white balls. The following experiment is repeated indefinitely: A ball is drawn from the urn; with probability a, the color of the ball is changed to the other color and is then put back in the urn, otherwise it is put back without change.
Let Xn be the number of black balls in the urn after n draws from the urn.

(a) Is Xn a Markov process? If so, find the appropriate transition probabilities.
(b) Do the transition probabilities depend on n?
(c) Repeat part a if a = 1. What changes?
(d) Repeat parts a and c if the urn contains K black balls and K white balls.

Igure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below: 4 quadrant coordinate grid showing two parallelograms. figure 1 has vertices at negative 5, 2 and negative 3, 4 and negative 4, 7 and negative 6, 5. figure 2 has vertices at 5, negative 2 and 7, negative 4 and 6, negative 7 and 4, negative 5. which two transformations can map figure 1 onto figure 2? reflection across the y-axis, followed by reflection across x-axis reflection across the x-axis, followed by reflection across y-axis reflection across the x-axis, followed by translation 10 units right reflection across the y-axis, followed by translation 5 units down