Answer
a. $1-P(A)-P(B)+P(A\ and\ B)$
b. $1-P(A\ and\ B)$
c. No
Work Step by Step
a. We first must subtract the probability of getting A and the probability of getting B from 1. However, if both A and B occurred, we would be counting twice, so we have to add back $P(A\ and\ B)$. Thus, we find: $1-P(A)-P(B)+P(A\ and\ B)$.
b. There are two options: either you don't get A or you don't get B, or you get both. Thus, we find: $1-P(A\ and\ B)$
c. They are not equal, for the probability that you don't get either is not equal to the probability that you don't get at least one of them.