Seven identical balls are randomly distributed among two urns. Step 1 of a game begins by flipping a fair coin. If it lands heads up, urn I is selected; otherwise, urn II is selected. In step 2 of the...

Seven identical balls are randomly distributed among two urns. Step 1 of a game begins by flipping a fair coin. If it lands heads up, urn I is selected; otherwise, urn II is selected. In step 2 of the game, a ball is removed randomly from the urn selected in step 1. Then the coin is flipped again. If it lands heads up, the ball will be placed in urn I. Otherwise, it will be placed in urn II. If this game is played successively, what are the long-run probability mass functions of the number of balls in urns I and II?