A scientific experiment consists of a sequence of 12 tests. Each trial of a test has...

 

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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? 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?

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