Question

Joe placed his pencil on point A of the hexagon below. He flipped a coin 4 times and recorded the sequence of heads and tails. Each time he flipped heads, he moved his pencil along one edge clockwise to the next vertex. Each time he flipped tails, he moved his pencil along one edge counter-clockwise to the next vertex. How much greater is the probability that he will end up with his pencil back on point A than the probability that he will end up with his pencil on point C? Express your answer as a common fraction.

Answer 1

Hexagon
D._______.E
/ \
C. / \.F
\ /
\ _________ /.A
B.

Answer 2

Whoops

Answer 3

I tried showing the hexagon

Answer 4

Well clockwise it’s like this, E,F,A,B,C,D

Answer 5

To get to C he needs H twice in a row
P(H,H) = 1/4