Three in a row

Probability Level 3

An unbiased coin is thrown. What is the expected number of tossings to obtain three heads in a row for the first time?

8 14 13 16

Theo-wpm Hermsen by Theo-wpm Hermsen , 66, Italy

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1 solution

If E = E = the expected number of tossings after which three heads in a row show up for the first time, then E = 1 2 ( E + 1 ) + 1 4 ( E + 2 ) + 1 8 ( E + 3 ) + 1 8 × 3 ⇒ E = 14 E = \frac{1}{2} (E + 1) + \frac{1}{4} (E + 2) + \frac{1}{8} (E + 3) + \frac{1}{8} \times 3 \Rightarrow E = 14

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