Consider the following system:

$->0\mathrm{.}71->0\mathrm{.}71->$

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

The system as shown.

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

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.

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.