Table 14-6
The following data consists of a matrix of transition probabilities (P)of four majors in the College of Business, and the initial proportion of students in each major π(0).Assume that each state represents a major and the transition probabilities represent changes from one major to the next after taking the introductory class in each discipline.
P =

π(0)= (.4, .3, .2, .1)
-Using the data in Table 14-6, determine Major 3's estimated popularity after students have taken the first two introductory courses.
A)0.232
B)0.220
C)0.356
D)0.191

Question

Table 14-6
The following data consists of a matrix of transition probabilities (P)of four majors in the College of Business, and the initial proportion of students in each major π(0).Assume that each state represents a major and the transition probabilities represent changes from one major to the next after taking the introductory class in each discipline.
P =
  
π(0)= (.4, .3, .2, .1)
-Using the data in Table 14-6, determine Major 3's estimated popularity after students have taken the first two introductory courses.
A)0.232 
B)0.220 
C)0.356 
D)0.191

Quizplus · Accepted Answer

The probability of a student majoring in Major 3 after taking the first two introductory courses is 0.232. This is calculated by multiplying the probability of taking Major 3 after the first course (0.356) by the probability of taking Major 3 after the second course (0.652).

Table 14-6 The Following Data Consists of a Matrix of Transition Probabilities