Show all your work $($typed in the document or pasting a scanned image of your handwritten solution$).$ Save your solution document in a $.$pdf file and upload it to Canvas along with an Excel file for calculations performed in Excel.

Problem $1(8$ points$)$:

The frequency of breakdown of a machine that issues lottery tickets is given in the following table. Repairs cost an average of $\backslash (\backslash$$ $236\backslash ).$ A service firm is willing to provide preventive maintenance under either of two options: number $1$ is $\backslash (\backslash$$ $506\backslash )$ and covers all necessary repairs, and number $2$ is $\backslash (\backslash$$ $378\backslash )$ and covers any repairs after the first one.

a: What is the expected cost for the two options?

b: Which option would have the lowest expected cost: pay for all repairs, or the service option?

$1.$ Pay for all repairs

$2.$ Service option Number $1$

$3.$ Service option Number $2$