About $80 \%$ of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents 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 variable $x$.
This is not a binomial experiment.
Baby recovers
Specify the value of $n$. Select the correct choice below and fill in any answer boxes in your choice.
A. $n=$
B. This is not a binomial experiment.
Specify the value of $p$. Select the correct choice below and fill in any answer boxes in your choice.
A. $p=$
B. This is not a binomial experiment.
Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.
Answer
Final Answer: This is a binomial experiment. A success is a baby recovering fully. The values of \(n\), \(p\), and \(q\) are as follows: \(n = \boxed{6}\), \(p = \boxed{0.8}\), \(q = \boxed{0.2}\). The possible values of the random variable \(x\) are \(\boxed{0, 1, 2, 3, 4, 5, 6}\).
Step 1 ：This is a binomial experiment because it meets all the criteria for a binomial experiment. The experiment consists of repeated trials (six babies), each trial can result in just two possible outcomes (a baby recovers fully or does not recover fully), the probability of success is the same on every trial (80% or 0.8), and the trials are independent (the recovery of one baby does not affect the recovery of another).
Step 2 ：A success in this experiment is defined as a baby recovering fully.
Step 3 ：The number of trials, denoted as \(n\), is 6 because there are six babies.
Step 4 ：The probability of success, denoted as \(p\), is 0.8 because there is an 80% chance of a baby recovering fully.
Step 5 ：The probability of failure, denoted as \(q\), is 1 - \(p\) = 0.2 because there is a 20% chance of a baby not recovering fully.
Step 6 ：The possible values of the random variable \(x\), which represents the number of successes, are 0, 1, 2, 3, 4, 5, and 6. These represent the possible number of babies that could recover fully.
Step 7 ：Final Answer: This is a binomial experiment. A success is a baby recovering fully. The values of \(n\), \(p\), and \(q\) are as follows: \(n = \boxed{6}\), \(p = \boxed{0.8}\), \(q = \boxed{0.2}\). The possible values of the random variable \(x\) are \(\boxed{0, 1, 2, 3, 4, 5, 6}\).
