John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw?  Select
A) 1/64 B) 2/16 C) 3/16 D) 7/16 E) 9/16
Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are   H-T-T-T-T-T ----&gt; P = (1/2)^7= 1/128   T-H-H-H-H-H ----&gt; P = (1/2)^7= 1/128   Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.   1/128 + 1/128 = 2/128 = 1/64   1/64nswer(1/64).
<result>A</result>
John throws a coin until a series of six consecutive heads or three consecutive tails appears. What is the probability that the game will end after the seventh throw?