About $60 \%$ of babies born with a certain ailment recover fully. A hospital is caring for six 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 $\mathrm{x}$.
Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.
A. $q=0.4$
B. This is not a binomial experiment.
List the possible values of the random variable $x$
$x=0,1,2, \ldots, 6$
$x=1,2,3, \ldots, 6$
$x=0,1,2, \ldots, 5$
This is not a binomial experiment.
Answer
\(\boxed{n=6, p=0.6, q=0.4, x=0,1,2,3,4,5,6}\)
Step 1 ：The experiment is a binomial experiment because it satisfies all the conditions of a binomial experiment. The experiment consists of n repeated trials, each trial can result in just two possible outcomes (a baby recovers or does not recover), the probability of success is the same on every trial, and the trials are independent.
Step 2 ：A success in this experiment is defined as a baby recovering fully from the ailment.
Step 3 ：The number of trials n is the number of babies, so \(n=6\).
Step 4 ：The probability of success p is given as 60% or \(p=0.6\).
Step 5 ：The probability of failure q is 1 - p, so \(q=1-0.6=0.4\).
Step 6 ：The possible values of the random variable x, which represents the number of successes, are all the integers from 0 to n, so \(x=0,1,2,3,4,5,6\).
Step 7 ：\(\boxed{n=6, p=0.6, q=0.4, x=0,1,2,3,4,5,6}\)
