To determine whether this is a binomial experiment, we need to check if it meets the following criteria:

1. Fixed number of trials (n): The experiment involves a fixed number of babies, which is 7 in this case.
2. Two possible outcomes per trial: Each baby can either recover fully (success) or not (failure).
3. Constant probability of success (p): The probability of a baby recovering fully is 50% (or 0.5) for each baby.
4. Independence of trials: The recovery of each baby is assumed to be independent of the others.

Given that all these conditions are satisfied, this is indeed a binomial experiment.

Identification of Components:

• Success: A baby recovering fully from the ailment.
• Number of trials (n): $n = 7$
• Probability of success (p): $p = 0.5$
• Probability of failure (q): $q = 1 - p = 1 - 0.5 = 0.5$

Possible Values of the Random Variable $x$:

The random variable $x$ represents the number of babies that recover fully. Since there are 7 babies, $x$ can take any integer value from 0 to 7. Thus, the possible values of $x$ are: $x = 0, 1, 2, 3, 4, 5, 6, 7$

Would you like to go into more detail or have any other questions?

5 Related Questions:

1. How do you calculate the mean and standard deviation of a binomial distribution?
2. What is the binomial probability formula, and how can it be applied to this scenario?
3. Can you calculate the probability that exactly 5 out of the 7 babies recover?
4. What is the cumulative probability of at least 3 babies recovering fully?
5. How would the binomial experiment change if the probability of recovery were not constant?

Tip: In a binomial experiment, the sum of the probabilities of all possible outcomes always equals 1. This can be a helpful check when calculating probabilities.