Answer:
it will take a programmer about 16.67 times to work before they are fired
Step-by-step explanation:
From the information given;
The transistion matrix for this study can be computed as:
P M X
P 0.7 0.2 0.1
M 0 0.95 0.05
X 0 0 1
where;
The probability that the programmer remains a programmer = ![(P *P)](https://tex.z-dn.net/?f=%28P%20%2AP%29)
The probability that the programmer turns out to be a manager = ![(P*M)](https://tex.z-dn.net/?f=%28P%2AM%29)
The probability that the programmer is being fired = ![(P*X)](https://tex.z-dn.net/?f=%28P%2AX%29)
Thus, the required number of years prior to the moment being fired for an employee y(P), for programmer and y(M) for manager is represented by ;
![y(P)=1+0.7y(P)+0.2y(M)](https://tex.z-dn.net/?f=y%28P%29%3D1%2B0.7y%28P%29%2B0.2y%28M%29)
![y(M)=1+ 0.95y(M).](https://tex.z-dn.net/?f=y%28M%29%3D1%2B%200.95y%28M%29.)
![0.05y(M)=1](https://tex.z-dn.net/?f=0.05y%28M%29%3D1)
y(M) = ![\dfrac{1}{0.05}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B0.05%7D)
y(M) =20
y(P)=1+0.7y(P)+0.2y(M)
y(P) - 0.7y(P) = 1 + 0.2y(M)
0.3y(P) = 1 + 0.2(20)=1+4
0.3y(P) = 1 + 4
0.3y(P) = 5
![y(P)=\dfrac{5}{0.3}](https://tex.z-dn.net/?f=y%28P%29%3D%5Cdfrac%7B5%7D%7B0.3%7D)
![y(P)=16.67](https://tex.z-dn.net/?f=y%28P%29%3D16.67)
Therefore, it will take a programmer about 16.67 times to work before they are fired