6 An airplane has four engines. On a flight from New York to Paris, each engine has a 0.001 chance of failing. The plane will crash if at any time two or fewer engines are working properly. Assume that the failures of different engines are independent.

a What is the probability that the plane will crash?

b Given that engine 1 will not fail during the flight, what is the probability that the plane will crash?

c Given that engine 1 will fail during the flight, what is the probability that the plane will not crash?