A broadcasting station has five major subsystems that must all be operational before a show can go on the air. If each subsystem has the same reliability, $($Round your answers to $4$ decimal places.$)$

$($a$)$ What reliability would be required to be $60\%$ certain of broadcast success?

$($b$)$ What reliability would be required to be $78\%$ certain of broadcast success?

$$ subsystem reliability

subsystem

$$ reliability

$($c$)$ What reliability would be required to be $51\%$ certain of broadcast $$ success? subsystem reliability