Are you sure the flight is safe?

Level pending

An airplane has 4 engines. The probability for the engines to function are \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{7}\) and \(\frac{7}{8}\) respectively. The airplane can fly if at least 1 of the engines can function. The probability that the airplane can fly safely can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b\)?

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