Simple (hopefully) probability question

[DCJ311]

Here are the prerequisites:

Hand A stands to win 1/3 of showdowns.
Hand B stands to win 2/3 of showdowns.
Ties are impossible.

Hands A and B do battle precisely 4 times.

What is the probability of:

A) Hand A defeating Hand B exactly 2 times out of 4.

B) Hand A defeating Hand B 2 or more times out of 4.

Any comments on how to do this problem are appreciated, as well as answers!