Consider the following system:

$0\mathrm{.}710\mathrm{.}71$

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 $\mathrm{.}71$ 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 $\mathrm{.}71$ and a switch that is $96$

percent reliable.

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

decimal places.