Problem $4$S$-1($Algo$)$

Consider the following system:

$\backslash (\backslash$rightarrow $0\mathrm{.}85\backslash$rightarrow $0\mathrm{.}85\backslash$rightarrow $\backslash )$

Determine the probability that the system will operate under each of these conditions:

a$.$ The system as shown.

Note: Do not round your intermediate calculations. Round your final answer to $4$ decimal places.

Probability

b$.$ Each system component has a backup with a probability of $\mathrm{.}85$ and a switch that is $100$ percent reliable. Note: Do not round your intermediate calculations. Round your final answer to $4$ decimal places.

Probability

c$.$ Each system component has a backup with a probability of $\mathrm{.}85$ and a switch that is $98$ percent reliable. Note: Do not round your intermediate calculations. Round your final answer to $4$ decimal places.

Probability