Question

The probability of successfully landing a plane using a flight simulator is p. Nine randomly

Answer 1

Success = p
failure = (1-p)  
is the correct first step.

To find the probability of at least one success, P(X>0), it is much easier to first calculate the probability of P(X=0)=NO success.  Then the complement of
P(X=0)'=1-P(X=0) = P(>0) = probability of at least one success.

By the multiplication rule,
P(X=0)=(1-p)^9
or the binomial distribution
P(X=0)=C(9,0)(p^0)(1-p)^9=1*1*(1-p)^9=(1-p)^9

So the probability of at least one success = 1-P(X=0)
=1-(1-p)^9