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All welders in a factory begin as apprentices. Every year the performance of each apprentice is reviewed. Past records indicate that after each review, 10% of apprentices are promoted to professional welder, 20% are terminated for unsatisfactory performance, and the remainder (70%) continue as apprentices.
(1) Draw the transition matrix.
(2) What is the probability that an apprentice is promoted to professional welder within 2 years? Within 4 years?
T^2=
T^4=
The probability that a random apprentice is promoted to welder in two years is 0.17 and that he is promoted to professional welder in four years is 0.2533.
All welders in a factory begin as apprentices. Every year the performance of each apprentice is reviewed. Past records indicate that after each review, 10% of apprentices are promoted to professional welder, 20% are terminated for unsatisfactory performance, and the remainder (70%) continue as apprentices.
(1) Draw the transition matrix.
| A | B | C | |
| A | 0.7 | 0.1 | 0.2 |
| B | 0 | 1 | 0 |
| C | 0 | 0 | 1 |
(2) What is the probability that an apprentice is promoted to professional welder within 2 years? Within 4 years?
T^2=
| 0.49 | 0.17 | 0.34 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
T^4=
| 0.2401 | 0.2533 | 0.5066 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
The probability that a random apprentice is promoted to welder in two years is 0.17 and that he is promoted to professional welder in four years is 0.2533.