The probabilities that machines X, Y, Z will be performing well are $\displaystyle \frac{1}{3},\frac{1}{4},\frac{1}{5}$. Find the probability that at most two of the machines will be operating.

P(at most two operating)

=1-P(all operating)

=$\displaystyle \frac{59}{60}$

This is found in my math book. Can anyone explain why we need to use 1-P(all operating)? and I found out this 1-P(all operating) cannot be used when finding P(all machines not working)... Why?