You are dealt one card at random form a full deck and your opponent is dealt $2$ cards (Without any replacement ). If you get an Ace, he pays you $10$ dollar, if you get a King, he pays you $5$ dollar (regardless of his cards). If you have neither an Ace nor a King, but your card is red and your opponent has no red cards, he pays you $1$ dollar. In all other cases you pay him $1$ dollar . Determine your expected earnings . Are they positive?