Suppose you and your friend play a game. In the game, (1) you randomly select 7 balls without replacement from Box A that contains 12 black balls and 16 white balls, (2) your friend randomly selects 5 balls without replacement from Box B that contains 9 black balls and 15 white balls You win the game if you get more black balls than your friend; otherwise, you lose the game. In addition, you assume that the number of black balls selected from one box DOES NOT affect the number of black balls from the other box. Therefore, the probability of selecting a black balls from Box A and y black balls from Box B can be calculated using the independent rule. P(x black balls from Box A and y black balls from Box B) = P(z black balls from Box A) x P(y black balls from Box B) Based on the assumptions above, calculate the following probabilities. Note: Round the Probability to at least 6 decimal places (0.123456) (1) You win the game with one black ball. Hint: You win the game with one black ball if your friend has no black balls. (2) You win the game with two black balls. Hint: You win the game with two black balls if your friend has at most 1 black ball. It is a good idea that makes a table to list all possible cases and to calculate the probabilities. # of black balls you have 2 ? # of black balls your friend has 0 ? Probability ??? ??? (3) You win the game with three black balls. (4) You win the game with four black balls.