A man lost in the woods decides to flip a coin, walking one mile east each time it appears heads and one mile west each time it appears tails. He flips the coin six times and walks accordingly. Find the probability that he will be at least two miles from his starting point at the end of this procedure.
+128408 There are 2^6 = 64 possibilites
He will be less than two milles from his starting point only when 3 heads and 3 tails occur in any sequence of 6 flips
So......
TTTTTT = 1 way
TTTTTH = 6 ways
TTTTHH = choose tails to occur in any four of six positions = C(6,4) = 15 ways
HHHHHH = 1 way
HHHHHT = 6 ways
HHHHTT = choose heads to occur in any four of six positions C(6, 4) = 15 ways
So......the probability =
2 [ 1 + 6 + 15 ] 22 11
______________ = ___ = ___
64 32 16
