We have three urns labeled 1, 2 and 3. The urns contain, respectively, three white and three black balls, four white and two black balls, and one white and two black balls. An experiment consists of selecting an urn at random then drawing a ball from it. Define the joint probability distribution over U and C, where U is the chosen urn with values 1, 2 and 3; and C is the color of the ball, with values black and white.
So far I have calculated as follows based on the fact that first we select random urn and then we select ball.
P(U = 1 , color = white) = 1/6 P(U = 1 , color = black) = 1/6 P(U = 2 , color = white) = 1/6 P(U = 2 , color = black) = 1/6 P(U = 3 , color = white) = 1/3 P(U = 3 , color = black) = 1/3
Is this correct?. I quite not sure on my approach. Need advice on this.