Question: 2014 Fall Final - 14
We flip a fair coin repeatedly and independently, resulting in a sequence of heads ($H$) and tails
($T$). We stop flipping the coin as soon as this sequence contains one $H$ or eight $T$s. What is
the probability that this sequence contains at most 7 $T$s?
(a)
None of the above.
(b)
$\sum_{k=0}^{7} (1/2)^{k}$
(c)
$\sum_{k=0}^{7} (1/2)^{k+1}$
(d)
$1 - (1/2)^{7}$