Suppose we now play a game: flip a fair coin until either tt or th first occurs. you win if tt comes up first, lose if th comes up first. since tt takes 50% longer on average to turn up, your opponent agrees that he has the advantage. so you tell him you’re willing to play if you pay him $5 when he wins, but he merely pays you a 20% premium, that is, $6, when you win. if you do this, you’re sneakily taking advantage of your opponent’s untrained intuition, since you’ve gotten him to agree to unfair odds. what is your expected profit per game?
a = 1/2 * (a + c) * h
a = 1/2 * (6 + (2 + 6 + 2)) * 6 = 48
30 / 0.350 = 85.7
you can fill up 85 bottles.