Refer to the KP&L sample points and sample point probabilities in the following tables.Completion Results for $40$ KP&L ProjectsCompletion Time $($months$)$SamplePointNumber ofPast ProjectsHaving TheseCompletion TimesStage $1$DesignStage $2$Construction$26(2,6)427(2,7)228(2,8)436(3,6)837(3,7)238(3,8)646(4,6)247(4,7)648(4,8)6$Total: $40$Probability Assignments for the KP&L Project Based on the Relative Frequency MethodSamplePointProjectCompletion TimeProbability ofSample Point$(2,6)8$ monthsP$(2,6)=440=0\mathrm{.}10(2,7)9$ monthsP$(2,7)=240=0\mathrm{.}05(2,8)10$ monthsP$(2,8)=440=0\mathrm{.}10(3,6)9$ monthsP$(3,6)=840=0\mathrm{.}20(3,7)10$ monthsP$(3,7)=240=0\mathrm{.}05(3,8)11$ monthsP$(3,8)=640=0\mathrm{.}15(4,6)10$ monthsP$(4,6)=240=0\mathrm{.}05(4,7)11$ monthsP$(4,7)=640=0\mathrm{.}15(4,8)12$ monthsP$(4,8)=640=0\mathrm{.}15$Total: $1\mathrm{.}00($a$)$The design stage $($stage $1)$ will run over budget if it takes $4$ months to complete. List the sample points in the event the design stage is over budget. $($Select all that apply.$)(2,6)(3,6)(4,6)(2,7)(3,7)(4,7)(2,8)(3,8)(4,8)($b$)$What is the probability that the design stage is over budget? $($c$)$The construction stage $($stage $2)$ will run over budget if it takes $8$ months to complete. List the sample points in the event the construction stage is over budget. $($Select all that apply.$)(2,6)(3,6)(4,6)(2,7)(3,7)(4,7)(2,8)(3,8)(4,8)($d$)$What is the probability that the construction stage is over budget? $($e$)$What is the probability that both stages are over budget?