Question

A sales organizer goes to.one of the three markets A,B and C every day. He never goes to the same market on consecutive days. If he goes to A, then the next day he goes to B. If he goes to either B or C then the next day he is thrice likely to go to A as to other market. If he goes to C on Thursday. Find the probability of his going to A on the next Tuesday.

Answer 1

probabilities of visits:

Friday: $P(A)=3/4,P(B)=1/4$

Saturday: $P(B)=3/4,P(A)=1/4\cdot3/4=3/16,P(C)=1/4\cdot1/4=1/16$

Sunday:

$P(A_1)=3/4\cdot3/4=9/16,P(A_2)=1/16\cdot3/4=3/64$

$P(B_1)=3/16,P(B_2)=1/16\cdot1/4=1/64$

$P(C)=3/4\cdot1/4=3/16$

Monday:

$P(A_1)=3/16\cdot3/4=9/64,P(A_2)=3/16\cdot3/4=9/64$

$P(A_3)=1/64\cdot3/4=3/256$

$P(B_1)=9/64,P(B_2)=3/16\cdot1/4=3/64,P(B_3)=3/64$

$P(C_1)=3/16\cdot1/4=3/64,P(C_2)=1/64\cdot1/4=1/256$

Tuesday:

$P(A)=9/64\cdot3/4+3/64\cdot3/4+3/64\cdot3/4+3/64\cdot3/4+1/256\cdot3/4=219/1024$