To solve this problem, we need to determine the probability that at least one of the four randomly selected births is a boy. Given the probability of a baby being a girl is 0.476, the probability of a baby being a boy is $1 - 0.476 = 0.524$.

The probability of at least one boy is the complement of the probability that all four babies are girls.

1. Calculate the probability that all four babies are girls: $P(\text{all four girls}) = 0.476^4$

2. Calculate the probability that at least one baby is a boy: $P(\text{at least one boy}) = 1 - P(\text{all four girls})$

Now, performing the calculations:

1. $0.476^4 = 0.476 \times 0.476 \times 0.476 \times 0.476 \approx 0.0516$
2. $P(\text{at least one boy}) = 1 - 0.0516 = 0.9484$

Thus, the probability that at least one of the four randomly selected births is a boy is approximately $0.948$ when rounded to three decimal places.

If you need further details or have any questions, please let me know.

Here are five questions you might want to ask next:

1. Can you explain how to calculate the probability of multiple independent events occurring?
2. How do you determine the complement of an event?
3. What is the binomial probability formula, and how is it used?
4. Can you solve a similar problem but with different probabilities?
5. How do these probabilities change with more births being considered?

Tip: When solving probability problems, always consider whether events are independent and whether you need to use the complement rule for simpler calculations.