The probability that a complex assembly line works correctly depends on whether the line worked correctly the
last time it was used. There is a 0.8 chance that the line will work correctly if it worked correctly the time before,
and a 0.7 chance that it will work correctly if it did not work correctly the time before. Set up a transition matrix
with this information and find the long-range probability that the line will work correctly.
Let the first state be the assembly line working correctly, and the second be that the assembly line does not work
correctly.
The transition matrix is P = $\boxed{}$ .
(Type an integer or decimal for each matrix element.)
The long-range probability that the line will work correctly is $\boxed{}$ .
(Type an integer or a simplified fraction.)