At a particular two-year college, a student has a probability of 0.39 of flunking out during a given year, a 0.08 probability of having to repeat the year, and a 0.53 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.) State 1 2 3 4 Meaning Freshman Sophomore 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 graduate. The expected number of years is. (Type an integer or decimal rounded to three decimal places as needed.) The probability that a freshman will graduate 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.
At a particular two-year college, a student has a probability of 0.39 of flunking out during a given year, a 0.08 probability of having to repeat the year, and a 0.53 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.) State 1 2 3 4 Meaning Freshman Sophomore 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 graduate. The expected number of years is. (Type an integer or decimal rounded to three decimal places as needed.) The probability that a freshman will graduate 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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:At a particular two-year college, a student has a probability of
0.39 of flunking out during a given year, a 0.08 probability of
having to repeat the year, and a 0.53 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.)
State
1
2
3
4
Meaning
Freshman
Sophomore
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 graduate.
The probability that a freshman will graduate 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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