I agree with you, but I am not sure about this:

P(A) * P(Not A) * P(Not A) = P(Not A) * P(Not A) * P(A)

P(A) > P(Not A) * P(Not A) * P(A)

Also, of course these are not independent events: if a plane has an accident for some reason, all the future flights take extra measures to avoid the problem that caused the accident and other related problems.