Accounts Receivable Have Been Grouped into the Following States

Essay

Accounts receivable have been grouped into the following states:
State 1: Paid
State 2: Bad debt
State 3: 0-30 days old
State 4: 31-60 days old
Sixty percent of all new bills are paid before they are 30 days old. The remainder of these go to state 4. Seventy percent of all 30 day old bills are paid before they become 60 days old. If not paid, they are permanently classified as bad debts.
a.Set up the one month Markov transition matrix.
b.What is the probability that an account in state 3 will be paid?