Absorbing Chain Problem

According to the University Registrar, a student's status (freshman, sophomore, junior, or senior) depends on the number of credits earned. According to (made-up) historical data:

A freshman has a 5% probability of staying as a freshman the following year, a 75% probability of becoming a sophomore, and a 20% probability of dropping college and never coming back (unfortunately!).

A sophomore has an 8% probability of staying as a sophomore the following year, a 77% probability of becoming a junior, and a 15% probability of dropping college and never coming back.

A junior has a 10% probability of staying as a junior the following year, an 80% probability of becoming a senior, and a 10% probability of dropping college and never coming back.

Finally, a senior has a 20% probability of staying as a senior the following year (super seniors!), a 75% of graduating, and a 5% probability of dropping college and never coming back.

a. What is the expected number of years a freshman will spend in college as a freshman, a sophomore will spend in college as a sophomore, a junior will spend in college as a junior and a senior will spend in college as a senior?

b. According to the answer above, what is the expected total number of years a new student starting next fall will spend in college?

c. What is the probability that a new student starting next fall will eventually graduate?

d. What is the probability that a student who is currently a junior will eventually graduate? If any, why do you think there a discrepancy