There are 3 coins which when flipped come up heads, respectively, with probabilities 1/4, 1/2, 3/4. One

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There are 3 coins which when flipped come up heads, respectively, with probabilities 1/4, 1/2, 3/4. One of these coins is randomly chosen and continually flipped.

(a) Find the expected number of flips until the first head.

(b) Find the mean number of heads in the first 8 flips.

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