MDFA, for binary strings congruent to (mod 8) for input $\sum$(0,1) as follow:
In here, binary string r(mod n),number of states is depends on remainder & final state is Qr.
from table 4 equal states such as Q0 =Q4 ,Q1 =Q5 ,Q2 =Q6,Q3 =Q7.
So MDFA contain 4 states.
Hi Thanks for the answer but recently I had discovered a flaw in your answer.
If you use 'Minimization of DFA' technique where we make 0equivalence,1equivalence states. You will not get q0 = q4, q1=q5,... as you have mentioned.
Your answer is correct but not the method.
The minimized DFA states after 'Minimization of DFA' are [q0],[q4],[q1,q3,q5,q7],[q2,q6].
where q0 is initial and final state and according to these minimized states we can say that "q0 and q4 are independent" and "q1,q3,q5,q7 are equal" and also "q2 and q6 are equal".
Please correct me if I am wrong.
The answer to the first probability question ...