You get 3 cards out of 52, the order doesn't matter.

a) What is the probability all 3 cards are spades?

b) What is the probability none of the 3 cards are spades?

a) I think it is

$\frac{{\textstyle (}\genfrac{}{}{0ex}{}{13}{3}{\textstyle )}}{{\textstyle (}\genfrac{}{}{0ex}{}{52}{3}{\textstyle )}}\approx 0.012941$

b) I know it is

$=\frac{{\textstyle (}\genfrac{}{}{0ex}{}{39}{3}{\textstyle )}}{{\textstyle (}\genfrac{}{}{0ex}{}{52}{3}{\textstyle )}}\approx 0.41353$

I know $P({A}^{c})=1-P(A)$

And if a is $A$ and b is ${A}^{c}$ the equation above is not correct..