About $20 \%$ of babies born with a certain ailment recover fully. A hospital is caring for seven babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of $n$, $p$, and $q$, and list the possible values of the random variable $x$.

Step 1 ：This problem is about binomial distribution. A binomial experiment has the following properties: The experiment consists of n repeated trials. Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. The probability of success, denoted by P, is the same on every trial. The trials are independent; the outcome on one trial does not affect the outcome on other trials.

Step 2 ：In this case, the experiment is about whether a baby recovers fully or not, which fits the definition of a binomial experiment. A success can be defined as a baby recovering fully.

Step 3 ：The number of trials, n, is 7 (the number of babies).

Step 4 ：The probability of success, p, is 20% or 0.2.

Step 5 ：The probability of failure, q, is therefore 1 - p = 0.8.

Step 6 ：The possible values of the random variable x (the number of babies that recover fully) can be any integer from 0 to 7.

Step 7 ：\(n = 7\)

Step 8 ：\(p = 0.2\)

Step 9 ：\(q = 0.8\)

Step 10 ：Possible values of x are \(x = 0, 1, 2, 3, 4, 5, 6, 7\)

Step 11 ：\(\boxed{\text{The experiment is a binomial experiment. A success is defined as a baby recovering fully. The values of } n, p, \text{ and } q \text{ are } n = 7, p = 0.2, \text{ and } q = 0.8 \text{ respectively. The possible values of the random variable } x \text{ are } 0, 1, 2, 3, 4, 5, 6, 7}\)