A small locally-owned hardware store in a western college town accepts both cash and checks for purchasing merchandise from the store. From experience, the store accountant has determined that 2 percent of the checks that are written for payment are "bad" (i.e., they are refused by the bank) and cannot be cashed. The accountant defines the following probability model \((R(X), f(x))\) for the outcome of a random variable \(X\) denoting the number of bad checks that occur in \(n\) checks received on a given day at the store:

\(f(x)= \begin{cases}\frac{n !}{(n-x) ! x !}(.02)^{x}(.98)^{n-x} \text { for } & x \in R(X)=\{0,1,2, \ldots, n\} \\ 0 & \text { elsewhere }\end{cases}\)

If the store receives 10 checks for payment on a given day, what is the probability that:

a. Half are bad?

b. No more than half are bad?

c. None are bad?

d. None are bad, given that no more than half are bad?