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How many flips to you need to see 3 heads in a row? Hint: you can either write one big recursive equation, or figure out how many flips for 2 heads first and use that.

Solution:

(1)   \begin{align*}E(1) & = 2 \\E(2) & = 2 + \frac{1}{4} \times 0 + \frac{1}{4} \times E(1) + \frac{2}{4} \times E(2) = 5 \\\end{align*}

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