Question

The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given year 70% of programmers remain in that position 20% are pro- moted to project manager and 10% are fired (state X). 95% of project managers remain in that position while 5% are fired. How long on the average does a programmer work before they are fired?

Answer 1

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 = $(P *P)$

The probability that the programmer turns out to be a manager = $(P*M)$

The probability that the programmer is being fired = $(P*X)$

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 ;

$y(P)=1+0.7y(P)+0.2y(M)$

$y(M)=1+ 0.95y(M).$

$0.05y(M)=1$

y(M) = $\dfrac{1}{0.05}$

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

$y(P)=\dfrac{5}{0.3}$

$y(P)=16.67$

Therefore, it will take a programmer about 16.67 times to work before they are fired