I have $n_1$ red balls in a box $A$. These balls are numbered from $1, \cdots n_1$. Let make a copy version of box $A$, called box $D$ (It means that the box $D$ will contain $n_1$ red balls from $1, \cdots n_1$).
Throw these balls to a box $B$ with loss probability $p$. Now, we change the color of these balls in the box B to green color.
Throw these balls from box $D$ and $B$ to a box $C$. The loss probability of balls in each box is also $p$. How many balls in box C will have the same number? Thank you so much