What will be the probability the second ball taken after first event would be red ?

Question

There are two bags. First contain 10 white balls and other contain 8 red balls. One ball from any bag shifted to other bag at random.
What will be the probability the second ball taken after first event would be red ?
First event is to drawn first ball.

Answer 1

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