Ans: 0.495 (49.5%)

There are 4 cases..

1)first event-white bag, second event- white bag

in this case probability will zero.

2)first event-white bag, second case-red bag

probability for this case:

1/2*1/2*8/9=0.222

3)first event-red bag, second event-white bag

probability for this case:

1/2*1/2*1/11=0.022

4)first event-red bag, second bag-red bag

probability for this case:

1/2*1/2=0.25

Finally add all these cases:

0.222+0.022+0.25= 0.495

Ans=0.495