In a frshman class of a college, there are 200 mathematics major students and 350 biology majors. Every year some math students think that genetics is fun, therefore, they are changing their majors to biology. Meanwhile, some biology students fall in love with math, therefore, they change their major to mathematics.
The probability of a student staying in math is 0.92, and the probability of changing from biology to math is 0.04. Assuming that the change of major happens only betwwen these two majors, answer the following questions:
a) What is the transition matrix?
b) How many of the students of this class are math majors in sophomore year?
c) How many of the students of this class will a biology senior ?