Mathematical probability problem, please explain!

There are three situations in which two balls are taken out of the first box and put into the second box:

1, all red, 5/9x4/8=5/ 18. Take any ball from the second box at this time.

The probability of getting a white ball is 5/18x5/(9+2) = 25/198.

2, all white, 4/9x3/8=3/ 18 At this point, take any ball from the second box.

The probability of getting a white ball is 3/18x7/(9+2) = 21198.

3. One red and one white, 5/9x4/8+4/9x5/8 =10/18 Take a ball from the second box at this time.

The probability of getting a white ball:1018x6/(9+2) = 60/198.

de:25/ 198+2 1/ 198+60/ 198 = 106/ 198 = 53/99。

The answer is 55/99. This is not right!