Professor Green gives two-month computer programming courses during the summer term. Students must pass a number of exams to pass the course, and each student is given three chances to take the exams. The following states describe the possible situations that could occur:1.
State 1: pass all of the exams and pass the course2.
State 2: do not pass all of the exams by the third attempt and flunk the course3.
State 3: fail an exam in the first attempt4.
State 4: fail an exam in the second attempt
After observing several classes, Professor Green was able to obtain the following matrix of transition probabilities:
At the present time, there are 50 students who did not pass all exams on the first attempt, and there are 30 students who did not pass all remaining exams on the second attempt. How many students in these two groups will pass the course, and how many will fail the course?