having to repeat the year, and a 0.56 probability of finishing the year. Use the states shown to the right to complete parts (a) through (c) below. (a) Write a transition matrix. Find F and FR. P= (Type an integer or decimal for each matrix element.) 134 F= (Type an integer or decimal for each matrix element. Round to three FR= (Type an integer or decimal for each matrix element. Round to three (b) Find the probability that a freshman will flunk out.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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At a particular two-year college, a student has a probability of State Meaning
0.30 of flunking out during a given year, a 0.14 probability of
Freshman
having to repeat the year, and a 0.56 probability of finishing
the year. Use the states shown to the right to complete parts
(a) through (c) below.
Sophomore
(a) Write a transition matrix. Find F and FR.
P=
(Type an integer or decimal for each matrix element.)
2
3
4
Has flunked out
Has graduated
F=
(Type an integer or decimal for each matrix element. Round to three decimal places as needed.)
FR=
(Type an integer or decimal for each matrix element. Round to three decimal places as needed.)
(b) Find the probability that a freshman will flunk out.
The probability that a freshman will flunk out is
(Type an integer or decimal rounded to three decimal places as needed.)
(c) Find the expected number of years that a freshman will be in college before graduating or flunking out.
The expected number of years is.
(Type an integer or decimal rounded to three decimal places as needed.)
Transcribed Image Text:Z nnect GB 1 et one J cAfee rity Sc... Firefox Old Firefo Data 1 At a particular two-year college, a student has a probability of State Meaning 0.30 of flunking out during a given year, a 0.14 probability of Freshman having to repeat the year, and a 0.56 probability of finishing the year. Use the states shown to the right to complete parts (a) through (c) below. Sophomore (a) Write a transition matrix. Find F and FR. P= (Type an integer or decimal for each matrix element.) 2 3 4 Has flunked out Has graduated F= (Type an integer or decimal for each matrix element. Round to three decimal places as needed.) FR= (Type an integer or decimal for each matrix element. Round to three decimal places as needed.) (b) Find the probability that a freshman will flunk out. The probability that a freshman will flunk out is (Type an integer or decimal rounded to three decimal places as needed.) (c) Find the expected number of years that a freshman will be in college before graduating or flunking out. The expected number of years is. (Type an integer or decimal rounded to three decimal places as needed.)
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