Call S(i) the number of valid sequences of i statements; as per the solution of the other problem, S(1)=2, S(2)=3, S(3)=5, and generally, S(i)=S(i-2)+S(i-1).
Call F(i) the total number of false statements taking into account all the possible sequences in S(i); F(1)=1, F(2)=2, and in general, F(i)=F(i-1)+F(i-2)+S(i-2). [To see why, see the solution to the other problem]
The average of false sentences is F(i)/(i*S(i)), which experimentally converges to about 0.27... [more on this to follow] so the answer we are looking for is 0.73... or 73%. |