Expected profit on a scratch ticket

A scratch ticket costs $2 to buy. It reveals three symbols drawn independently, each of which is a star with probability 14\tfrac14. The ticket pays $50 if all three symbols are stars, and nothing otherwise. What is your expected profit per ticket (payout minus the $2 cost), in dollars to four places?

Show hints (2)+
  1. All three stars: multiply the independent chances, (1/4)3(1/4)^3.
  2. Expected payout is 50(1/4)350\cdot(1/4)^3; profit subtracts the $2 cost.

Answer

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-1.2188 (± 0.001)

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Asked at: Timed Mental-Math & Sequences, ETF Market-Making

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