60% pass a test and 40% fail, then 80% pass and 20% fail, What is the probablilty of passing test 2?

Question

60% pass a test the first and 40% fail, the second time 80% pass and 20% fail, the third time 90% pass and 10% fail.  What is the probablilty of passing the 2nd time?

Answer 1

60% pass the test first time. Of the 40% that fail, 80% pass on the second attempt, so that's 0.4×0.8=0.32=32%. The probability of passing on the second attempt is therefore 32%. 

If we take 1000 examinees as the start:

1st attempt: 600 pass, 400 fail (60% of 1000 pass)

2nd attempt:                 320 pass, 80 fail (80% pass of the 400 who failed before)

3rd attempt:                                   72 pass, 8 fail (90% pass of the 80 who failed)