There are two propositions: (a) i flip a coin, if it is heads, you are paid $3; if it is tails, you are paid $0. it costs you $1 to participate in this proposition. you may do so at any level, or repeatedly, and the payoffs scale accordingly. (b) you may keep your money in your pocket (earning no interest). here is a third proposition: (c) i flip the coin three times. if at least two of the flips are heads, you are paid $27; otherwise zero. how much is this proposition worth?