A casino game has three possible winnings, $\$15$, $\$10$, and $\$5$, each being twice as likely as the one before it. Player's don't win anything $65\%$ of the time.
i) If it costs $\$3$ to play this game, how much does a player expect to lose on average? (find the expected profit, which will be negative. This is the player's loss).