A die decides how many balls to draw

You roll a fair six-sided die to get a number NN, then draw NN balls with replacement from a bag in which exactly one quarter of the balls are gold. You win $1 for each gold ball drawn. What is the expected winnings (in dollars, to three decimals)?

Show hints (2)+
  1. Given N draws, expected gold = N/4; then average over the die.
  2. Tower rule: E[W] = (1/4)·E[N], with E[N] = 3.5.

Answer

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0.875

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Asked at: Timed Mental-Math & Sequences, EV & Betting Games

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