Define the following events:

S : Success
R1: Selecting a red ball from first container
R2: Selecting a red ball from second container
R0: NOT selecting a red ball from first container

Symbols:
    * is intersection
    + is union

And note that R0 and R2 are independent events, i.e., P(R0.R2) = P(R0)P(R2)

Now,

P(S) = P{R1+ (R0.R2)} = P(R1) + P(R0).P(R2) = (8/10) + [(2/10)(5/10)] = 0.9