Exercise $2.$ A daily truck rental company in Memphis has three locations:

$S_1($downtown$),S_2($airport$)$ and $S_3($North Memphis$).$ Customers may pick up a truck at any of the branches and return it to any other.

Experience has established the following drop$-$off pattern:

$60\%$ of trucks rented downtown are returned to the downtown office; $30\%$ are dropped of at the airport office and $10\%$ are returned to the North Memphis office.

Of trucks rented at the airport, $20\%$ are returned downtown, $50\%$ at the airport and $30\%$ in North Memphis.

For trucks rented at the North Memphis office, $20\%$ are returned downtown,