Question

Refer to exercise 12. let z = x + y represent the total number of repairs needed.

Answer 1

Assuming the question I linked is the same as yours, you should have the following information (provided you completed exercise 12):

$\mu_X=1.01$
$\mu_Y=1.23$
$\sigma_X\approx0.89994$
$\sigma_Y\approx0.99855$
$\mathrm{Cov}(X,Y)\approx0.2377$
$\rho_{X,Y}\approx0.264512$

Given that $Z=X+Y$, we have

$\mu_Z=\mu_X+\mu_Y=2.24$

$\sigma_Z=\sigma_X+\sigma_Y+2\,\mathrm{Cov}(X,Y)\approx1.51076$

Finally, $Z=2$ is the same as the event that any one of the following occurs: $X=0$ and $Y=2$; $X=1$ and $Y=1$; or $X=2$ and $Y=0$. So we have

$\mathbb P(Z=2)=0.02+0.16+0.07=0.25$