Probability of stacked medication working Say we're talking about contraception, and the probability of one contraceptive, $A$, working is $99\%$, and the other, $B$ is also $99\%$. What is the probability of them working using both at the same time?
When I tried raising 99% to the power of 2, I realized I only got the effectiveness rate of contraception used at two separate events. Other similar operations haven't worked. 
So I'm not sure what else to do here.
Edit: I'm aware medical statistics are extremely complicated, so I'm only assuming independent conditions for conventional purposes to get some idea of what the probability looks like.
 A: The method has worked if one of them worked or both worked. In short, 
$$P(\text{method worked}) = 1-P(\text{both failed})$$
$$= 1-(0.01)^2$$
Edit: 
I have assumed the two methods were independent when I said $P(\text{both failed}) = 0.01\times 0.01$
A: By inclusion-exclusion, the probability that at least one measure works is equal to
\begin{align}
P(\text{$A$ or $B$}) & = P(A) + P(B) - P(\text{$A$ and $B$}) \\
                     & = 1.98 - P(\text{$A$ and $B$})
\end{align}
If $A$ and $B$ are independent, then by definition,
$$
P(\text{$A$ and $B$}) = P(A)P(B) = 0.9801
$$
and then
$$
P(\text{$A$ or $B$}) = 1.98-0.9801 = 0.9999
$$
as in Vizag's answer.  Otherwise, we need to account for dependence between $A$ and $B$, as represented in the foregoing expression by $P(\text{$A$ and $B$})$.

As is conventional in logical terminology, the use of "$A$ and $B$" and "$A$ or $B$" are logical connections.  The conjunction "$A$ and $B$" means "$A$ is true and $B$ is true," while the disjunction "$A$ or $B$" means "$A$ is true or $B$ is true."  In this case, the former does not mean "the physical combination of $A$ and $B$ works."  (Note that it is difficult to come up with a meaningful interpretation of "the physical combination of $A$ or $B$.")
