(Solved): A deck of six cards consists of three black cards numbered 1,2,3, and three red cards numbered 1, 2 ...

A deck of six cards consists of three black cards numbered $1,2,3$, and three red cards numbered 1, 2, 3. First, Vann draws a card at random and without replacement. Then Paul draws a card at random and without replacement from the remaining cards. Let $A$ be the event that Paul's card has a larger number than Vann's card. Let $B$ be the event that Vann's card has a larger number than Paul's card. (a) Are $A$ and $B$ mutually exclusive? (b) Are $A$ and $B$ complements of one another?