If you flip a fair coin four times, what is the probability of flipping at least three heads in a row?

It says "three heads in a row". So this makes me think the only possibilities are HHHT, THHH, and HHHH for 3/16. What do we think? Am I missing something?

  • 1
    $\begingroup$ Your work is correct. $\endgroup$ – N. F. Taussig Sep 17 '17 at 2:09
  • $\begingroup$ You are correct. It'd get more applied if it were at least n heads out of m. Then your method would require more finesse $\endgroup$ – fleablood Sep 17 '17 at 2:49

We need to add all of the probabilities of events that satisfy our criterion.

$$\begin{align} \text{tot. prob.} &= P(HHHT) + P(THHH) + P(HHHH) \\ &= \frac12 \frac12 \frac12 \frac12 + \frac12 \frac12 \frac12 \frac12 + \frac12 \frac12 \frac12 \frac12 \\ &= \frac{3}{2^4} \\ &=\frac{3}{16} \\ \end{align}$$

So you were spot on! $\ddot\smile$


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