Players A and B are playing a game of drawing coins from two boxes without returning/replacing them. Box1 has three coins with values 0, 1 and 2 and Box2 has two coins with values 1 and 2. In the game, each draw Player A chooses one of the two boxes randomly (with 1/2 chance) and Player B draws a coin from that box. After two draws, the drawn coins go to one of the players - if the sum is greater than 2, Player A gets the coins or else Player B gets the coins.
Yi - random variable which signifies the outcome of i-th draw (i = 1,2)
I need to find the distribution of the random vector (Y2,Y1)
I can find out the probabilities of the first draw with the formula for total probability, but I'm having trouble with the second.
Can anyone help me?