To solve this problem, we need to find the probability that at least one of the seven randomly selected babies is a girl.

Step 1: Understanding the problem

The probability of a baby being a boy is given as $P(\text{boy}) = 0.516$. Therefore, the probability of a baby being a girl is: $P(\text{girl}) = 1 - P(\text{boy}) = 1 - 0.516 = 0.484.$

Step 2: Probability of the complement event

The complement of "at least one girl" is "no girls," meaning all seven babies are boys. The probability of all seven babies being boys is: $P(\text{all boys}) = (P(\text{boy}))^7 = (0.516)^7.$

Step 3: Calculate the complement

Now, we calculate $(0.516)^7$.

$P(\text{all boys}) = 0.516^7 \approx 0.021.$

Step 4: Probability of at least one girl

The probability of at least one girl is the complement of all seven babies being boys: $P(\text{at least one girl}) = 1 - P(\text{all boys}) = 1 - 0.021 = 0.979.$

Final Answer:

The probability that at least one of the next seven babies is a girl is approximately: $\boxed{0.979}.$

(Rounded to three decimal places as required.)

Would you like more details on any step, or have any other questions?

Here are 5 related questions for further understanding:

1. How do we calculate the probability of exactly one girl in seven births?
2. What is the probability of exactly three boys in seven births?
3. How would the solution change if the probability of a boy was different?
4. How can we generalize this method for more or fewer births?
5. What is the binomial distribution, and how is it relevant here?

Tip: Always double-check if the problem asks for at least, exactly, or no occurrence when calculating probabilities!