$4.$B$.6$ A scientific experiment consists of a sequence of $12$ tests. Each trial of a test has a $30\%$ chance of passing, and a successful attempt of a test is required to move on to the next test. The success of a test is a mere coincidence every time, so the lab technician cannot gain experience or skills in it$.$ After $20$ attempts, the third of the twelve tests was reached: $7$ attempts were needed to pass the first test, $6$ attempts for the second and the first $6$ attempts of the third test all failed. What is the expected total number of test attempts required to complete the entire experiment?